Lessee...
The MV penalty is a minus to your piloting roll. If your piloting roll exceeds their attack roll, they miss, basically. If they hit, the larger the difference between your roll and theirs, the more damage you're going to take. If two mecha, both with -1 MV are standing still, they both dodge attacks at the same rate, so far as I know. Providing, of course, if they're both scale 2 machines vs. scale 2 weapons, and there's nothing else involved, like ECM or whathaveyou. The faster you move, though, the harder it is to hit; for every X amount of units per time (Dun remember/never bothered to find out the exact formula) you're moving, they receive a penalty to their attack roll against you.
The one thing you're going to want, eventually, is to not stop moving, especially later on when you're heavily outnumbered. Certain builds can cut down on that reliance (Hull down, monsterous, etc), but it's generally not worth it to do so. The TR penalty's not as big of an issue when you get a good tarcomp into your machine and get gunnery/artillery up a bit. Effectively, the +3 you get to accuracy when still isn't really worth the +3 they get for shooting at a non-moving target, and the potentially massive penalty they get when shooting at a moving target is entirely too big an issue to ignore.
Short theory craft here: You stop to fire; you get +3 to accuracy. There's 3 enemies; you manage to oneshot one. The other two both now have +3 versus you. Your number juggling is at a net -3, to your loss. The larger the numbers (and you'll likely end up fighting 6+), the bigger that cumulative loss becomes. Were you moving, though, you'd instead get no bonus to accuracy, but each enemy gets a variable penalty to attack you. You might not oneshot that mecha, but they're all just got at least -1 to hit, getting a net balance of 0; and more likely than not, you're going to be giving them a much bigger penalty than -1, each point beyond further tilting the numbers game in your favor.
Yeah, the dodge skill is SF:0, or at least, when you're not in a machine. Mecha Piloting determines your chance to avoid a hit in SF:1+ fights.
Sensors primarily govern missile attacks, that is mlauncher weapons (Nukes, Swarm Missiles, etc.). I don't remember if they effect your sight range, but they're not going to have any effect on how well you hit things with those phase cannons. I think you need one to avoid a penalty, but the class doesn't really matter if you're not using missiles. Of course, your sensor rating is entirely dependent on the sensors themselves, which can make missiles a good choice when you've tanked your TR score all to heck.
ECM is an extra defensive roll vs ranged attacks. Iirc, the number on that is (ECM Class - 5) + your electronic warfare score, vs... something or other, I forget what. So you'll need at least a class 6 ECM or 5 EW to start seeing a benefit, though even a negative modifier has a chance to help out. Your craft score factors in there, too, though primarily through the EW skill. At least that's the formula in GH2, and I don't think it's been changed yet.