As Sea-Envy said, that’s a “no” to all of those. That said, it’s a very easy power to justify putting in a pool for Defend actions and many types of Overcomes, offers you some unusual mobility options, and depending on how your character and GM have agreed to define it can be a means of making “exotic” Attacks that bypass both physical and energy damage resistances (which are regrettably rare on actual villains, who more often just get “resist everything” tricks). If you want something closer to the kind of resistance you’re talking about, take Principle of Indestructibility (under Expertise Principles) and define it as being tied to your Intangibility power rather than (say) being more traditionally invulnerable thanks to bulletproof skin or power armor or a force field or whatever. That’ll help even more with using it for Overcomes too.
Just in general, powers never require an action to turn on or off, and there’s nothing restricting you from using several in a turn when describing what you’re trying to do, which then defines the mechanics of your turn. Only one of them will put a die into your pool, but you can certainly do things like using Intangibility to ghost through a wall behind a villain and Electricity to stun them - and if you had a “-4 Blinded” penalty on you, you could make a case for using Awareness to ignore it for the action thanks to your literal radar sense making vision irrelevant. Having described it narratively, which power contributes a die (and even what type action you’re taking) is mostly up to you, although the GM might veto a bad matchup. For ex, if your main goal is landing damage on the target, that’s probably an Attack action (whether as part of an ability or just basic) and Electricity is probably key - unless the target’s got some kind of armor that Intangibility will let you reach past, in which case it might be key. If you’re more interested in literally stunning the target rather than taking them out of action for good, that’s probably a Hinder instead, with similar justifications for which power is key. You might even work in Awareness instead if you’re trying to put your zap into a precise spot, maybe a gap in their defenses that your radar sense has picked out. Of course, ideally you have an ability that lets you Attack and Hinder in one action, and if not you could always up to take a twist for a risky basic to accomplish that as instead.
And with Intangibility it’s also easy to describe yourself as phasing past any counterattack, justifying an ability or risky basic that combines (say) Attack and Defend actions. That’s not total invincibility, but it models one of the power’s potential advantages reasonably well. All depends on how you describe what you’re attempting to do and what sounds good to the GM.