Disclaimer: Yes, this is the first time I've ever written a guide. Yes, I would appreciate it if you don't completely eat me alive. And yes, I 'borrowed' Flamethrower's format (I hope you don't mind!) because I found it to be the easiest way to understand.
Enjoy *bow*
Mr. Fixer: DIY
Introduction
Mr. Fixer is the resident martial arts master of the multiverse (as well as a pretty good car mechanic), wielding a variety of tools in a myriad of styles to bring down the baddies. He is a mostly a support character, with some damaging options. If you want versatility, the ability to tweak things to your, and your teammate's, advantage, or you just want to be Mr. Miyagi for an hour or so, then this is the hero for you.
*Mr. Fixer may be the most controversial hero in the game; there are more posts about "fixing" Mr. Fixer than any other character. Played properly, however, Mr. Fixer has the potential to fix any situation that can come up in a game.
Attack
Mr. Fixer isn't exactly big on damage. More often than not, it's better to leave the damage dealing to your teammates and concentrate on making them more effective. But don't get me wrong: if the situation calls for it, Mr. Fixer can deal damage to take out a particularly annoying baddie, or especially to the Chairman and the Operative.
Charge and Overdrive are your typical one-shot attack card, if for a little less damage than usual. I find that I use this card to spread the love around (Charge one target, then Strike another, or Strike two targets), more than just a means to deal an extra few damage to the same target. It can, however, take out an enemy in a pinch, especially when boosted with your Tools and Styles. And while Overdrive is like a poor man's Charge (using Strike twice basically comes to a 1 damage Charge), it is special in that, if you have an Infection, or a Treasure from the Tomb of Anubis that lets you use another Power, you can play Overdrive, use the Treasure's/Infection's power, and then use Strike twice.
Harmony lets you pump up the damage, helping you try to get over the soak most Villains have. It also makes for good on-going fodder; when an environment cards makes me get rid of an on-going "or suffer the consequences", I, as a rule, choose to get rid of Harmony rather than a style card (unless, of course, I have a copy of that same Style in my hand, ready to go)
Bloody Knuckles is the definition of a double edged sword, and more often than not, I find that it hurts a lot more than it gives. Of course, if damage dealt to him is somehow reduced (Hello there, AA), or if he is allowed to use Strike out of turn (hello again, AA), then it becomes much more palatable. As a general rule, though, the Villain/Environment is able to make much more use of the +2 damage to him than Fixer is able to make use of the +2 damage he gains.
Tools and Styles
Simply put, Mr. Fixer isn't playing the same game as other heroes. As it has been mentioned before, his role is to fix situations, tweaking them a little so his teammates can take down the baddies. More often than not, Fixer has the solution for the situation somewhere in his deck. He accomplishes this by using a variety of Tools and Styles, putting them together to achieve almost ridiculous combos. It is important to note that you can only have one Tool and one Style in play, though you can trade these up (Tools go back to the hand, but Styles are outright sent to the trash)
Jack Handle: This card is good against any Villain with a lot of minions; boosted, Mr. Fixer can take them all down in one blow. This is especially ridiculous against Plague Rat (correct me if I'm wrong but) whenever you would deal damage to yourself for Infection, you deal that much irreducible damage to the Rat and anything else than might be out instead!
Use when: many minions, targets out, and you want to take them all out at once (Citizens, Relics, etc), against Plague Rat
Good with: Alternating Tiger Claw, Riveting Crane, Grease Monkey Fist
Pipe Wrench: This one is actually my "default" tool- if the situation doesn't call for anything specific, one can always use DR to keep Fixer around longer.
Use when: you want to keep Fixer alive longer, no need for any other specific tool
Good with: Driving Mantis
Hoist Chain: Useful against Spite, the Operative, The Matriarch, and the like. Reducing your opponent's damage is always useful, especially when getting ready for a big move, such as taking out all the Fowl from the board.
Use when: the opponent has revenge damage, villain likes to plink you, uses multiple instances of damage
Good with: Alternating Tiger Claw, Greased Monkey Fist
Dual Crowbars: Basically Jack Handle, except you can only hit two, and you get +1 damage. Useful if there are less minions on the board, or you want to hit only two at once.
Use when: two targets to hit, useful to punch through DR
Good with: Grease Monkey Fist
Tire Iron: For me, the least obviously useful Tool. Projectile damage is okay, and being able to take out anything with 3 or 4 life left is good (provided they don't have DR), but the situations I find this useful are few and far in between.
Use when: you want to take down something with low health (Tome of the Unknowable comes to mind), good against DR
Good with: Grease Monkey Fist, Alternating Tiger Claw
Alternating Tiger Claw: My favorite style. This lets him push all of his attacks through, no problem, letting you get at the effects immediately.
Use when: you need to push through DR to get an effect NOW.
Riveting Crane: Like ATC, but for your teammates. Especially good if you have some low damage but high frequency teammates (Fanatic and Chrono Ranger come to mind) that need to get past DR. The only problem is getting through the DR yourself, but that's where your own +1's come in.
Use when: low damage, high frequency teammates
Driving Mantis: My default style, to keep Fixer alive until he is needed. Very good with Pipe Wrench: someone hits you for 3, it gets reduced to 2, so you can throw it right back at your opponent for three. Another good one would be to use the second hit from Dual Crowbars to hit yourself, then using Driving Mantis to redirect it right back at your opponent.
Use when: default style, Villain likes to hit you for little bits of damage
Grease Monkey Fist: Very useful, especially against things with melee immunity. Imagine taking down an entire dreadnought with a pipe wrench.
Use when: you need an extra +1 damage, against immune to melee enemies
It is important to understand that you shouldn't just lay down a Style, then a Tool, and that's it for you. You should be willing to switch around, adapting to situations. Unlike other heroes, Mr. Fixer doesn't have an "Ultimate Set-up" to work towards-he works in the moment.
Utility
Fixer has two search cards. Meditation allows you to find the exact style you need, whether from the trash or the deck, effectively representing any Style in your entire deck. Tool Box gives you good drawing abilities to get at those tools. It is entirely possible with an early Tool Box to end up with half the deck in your hand.
Salvage Yard will make your fellow heroes weep with joy, especially equipment heavy heroes such as the Wraith or AZ. This one is particularly heartening after, say, a Devastating Aurora takes out everyone's hard work. Allowing you to use Overdrive in that same turn just adds icing to the cake. Unfortunately, Fixer himself has less use of the equipment recovery since his Tools go back to his hand when replaced by another Tool.
Grease Gun may be Fixer's ultimate fix: a round of relatively complete safety (barring equipment destruction) basically for free. There is no situation where this card is useless, and indeed, this card has saved my team from utter destruction many times. If there is a card for Fixer to save and reuse over and over again, it's this one.
Weaknesses
As is constantly complained about, the greatest weakness of Fixer is not having the right tools for the right job. Although he has excellent search abilities for Styles, Meditation being any style you want for free, he has no such specific search card for Tools; he relies on the drawing power of Tool Box to hunt for them. This slows down Fixer quite a bit, as there is every chance that the Tools he needs are hiding out somewhere at the bottom of his deck. In practice though, I haven't personally had a game where Mr. Fixer was absolutely useless. Sure, there may be games where he isn't functioning optimally, but Fixer will always be able to bring something to the board. You just have to do the best you can with what you have (which, I think, makes sense considering he's an auto mechanic.)
I also want to point out that Tools, unlike Styles, go back to your hand upon replacement. This lets you keep all your tools in hand, in case you need them later. You don't really have to worry about losing your tools, only getting them in the first place.
Fixes
As stated above, several Fixes have been suggested to make Fixer more palatable. One suggestion made by j1hopki1 is to change Strike to read "You may discard a card. If you do, Mr. Fixer deals one target 2 melee damage. If don't, Mr. Fixer deals one target 1 melee damage." This, by itself, makes it easier for Mr. Fixer to contribute, as well as to punch through DR for Riveting Crane, while thematically making sense: sometimes, a martial artist has to sacrifice form to brute strength. This adds a level of choice previously unknown to Fixer: "Do I save this card for later, or can I burn it for extra damage?".
Another good fix is the one suggested by Spiff, the Stance Shifting Master version, available on his site. This fix gives Fixer a Bruce Lee kind of feel, further encouraging players not to stick to just one Tool/Style combination.
The last good fix I will discuss is a suggested change to Toolbox. Keeping the text as is, we add "Power: Search Mr. fixer's deck for a tool and place it into play or into your hand. Shuffle your deck. Destroy this card.". This gives him a good search card for Tools, but at the same time, comes at a good, reasonable cost: "Do I absolutely need a particularly Tool right now, or do I use this draw engine for just a little while longer?".
Teamups
As already stated above, increasing Fixer's damage, letting him punch through DR to work his magic is very good for him, so any hero who helps in this regard would work well with Fixer. He is also best friends with any hero who helps him draw cards, so he can get at his Tools and Styles faster.
Nemeses
Mr. Fixer has the dubious honor of having arguably one of the toughest Villains as a nemesis: The Chairman and the Operative. Playing against them with Fixer somewhat changes his play style; although he is still primarily concerned with fixing situations (example: his Alternating Tiger Claw/Greased Monkey Fist and Jack Handle work wonders against the hoards of underbosses and thugs the Organization throws at you, Hoist Chain takes care of revenge damage, Tire Iron can take care of DR protected underbosses, Mantis+Pipe Wrench can keep you alive...) he becomes more aggressive. I find that when I use him against the Organization, I focus on making full use of the nemesis bonus and just plain dealing damage more than usual (For example, I am a lot less hesitant to drop Bloody Knuckles, though again, this also means that I get beaten up badly as well).