Ah yes, Omnitron. He can be really easy, or he can kick your arse (as you've already seen ;)). Yes, the Electro-Pulse thingy can be a right bummer. Kicking it down a bit so it at least does less damage is helpful, if you can't stop it being played in the first place.
Personally, I find Omnitron is one of those villains where you deck control really, really helps - apart from the Electro-Pulse there's also Sedetive Flechettes (destroys all Ongoings) and erm, Technological Singularity I think it's called (destroys all Equipment and then I think deals damage to each hero based on how many cards of their was destroyed). There's also Terraforming (destroys all Environment cards, then deals damage equal to the number of cards destroyed), though I've never had more than two or three Environment cards out when this has come up.
A couple of base decks good for deck control are the Wraith (Infra-Red Eyepiece) and Visionary (her deck is pretty much made for controlling stuff). If you have Infernal Relics, I cannot recommend Nightmist enough as a good character :D. She is my favourite and I've never lost a game playing her - as far as deck control is concerned, Astral Premonition (Ongoing, Power = Look at top two cards of a deck, put one on the top and one on the bottom) and Mistbound (One-Shot - Discard two cards, then choose a deck - cards can't be played from that deck till the start of your next turn) are the ones to go for.
There are also a few cards that can at help with repelling damage. Assuming Omnitron doesn't manage to destroy your stuff, Legacy is good for this. With Next Evolution (Choose a damage type - you are immune to that damage till the start of your next turn) and Lead From the Front (any time a hero would be damaged by anything, you can choose to redirect that damage to Legacy) you can totally nullify any damage coming from the Electro-Pulse. There's also a card of Tachyon's. I don't recall the name…might be Hyperspeed Assault or something. Anyway, it hits all non-hero targets for one point of damage. Woo, sounds epic, right? But the other effect of the card is that any target damaged in that way can't deal damage till the start of Tachyon's next turn.
Unless you have access to Mistbound, you cna't always stop Omnitron playing nasty cards. This is because I think pretty much all "look at Villain card" powers only let you control what the top card will be, since generally you can look at the top two or three, but then you only get to put one of those on the top and the rest on the bottom. Since in one mode, Omnitron gets to draw two cards in his turn, this means you can never be sure the second card will be a less-nasty one. If you have Nightmist and she has enough control over her deck to be able to have a copy of Mistbound (she has two) in-hand every time that turn comes around, you can get her to play it so that on his two-card turn, Omnitron can't play anything. Every other turn you can (again, if using Nighmist) just use Astral Premonition to control what the top card will be. Or get Visionary or the Wraith or whoever to do that, since they have the ability (as mentioned above).
Another character who might help is the other Infernal Relics one, the Argent Adept, who has the "emergency use" card of "Destroy an instrument, then destroy any card other than a character card", which you could use to insta-nuke any single card that comes out which might otherwise cause you some serious problems.
Another plus for Tachyon against Omnitron, actually, is that she's pretty good in that she has only one equipment card (her HUD Goggles), so Omnitron's stuff-destroying cards aren't much of a threat. There's also the fact that she can burn through her deck pretty fast and potentially do about 70 damage in a single turn. Okay, Haka and Bunker can do this too (with Savage Mana and Omni-cannon, respectively), but both their methods involve keeping the card in question in play, something that can be messed up nicely if Omnitron draws Sedetive Flechettes or the Technological Singularity. For Tachyon, try and get as many Burst cards into her trash as you can. I think she has 23 in all. Meanwhile, save up all three copies of Lightspeed Barrage and both copies of erm…something Reflexes. Both are One-Shots, but aren't Bursts. With your goggles in play as well, you can use these cards to play all three Lightspeed Barrages in one turn. Lightspeed Barrage hits a single target for damage equal to the number of Burst cards in your trash. So if you've got all (I think) 23, that's 69 damage in a single turn. And then you can still play another card after that, if you get the order right :D.
Yeah, the characters I'm less keen on don't get much play time, but the ones I prefer…well, I've managed to find which techniques work best against most villains >:).
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