"MIG" stands for "metal inert gas." A wire feed without gas is not a MIG, and I don't think you'll get good results on a bike frame with it. I would hesitate to do even MIG except for experimenting. One of the reasons bike frames are done with TIG, I think, is that it gets high penetration very quickly, thus allowing welding on tubing that has already been heat-treated.
You can get a pretty nice MIG welder that runs on 115 volts, and that would be plenty for bicycle work, but a stretch for some of the other projects you're contemplating. Control arms? I wouldn't try it with a little wire-feed!
Of course if you're just making gaspipe frames for practice and to test out shapes and sizes, you could probably make one that works with just about any welder, but you won't be making a fine quality frame, or anything even close. If you want to make good frames of good material and can't get into TIG, the best alternative would be to learn to braze. Of course that requires gas too, but you can braze just about any frame material without killing it.
To get a functional 220 outlet from your house, you need, first of course, access either to the fuse/breaker box, or to a high amperage outlet that already exists. You might be able to run a 220 welder from a dryer outlet, but it will probably pop breakers when you get up into the higher ranges. Most 220 "buzz-box" welders want a 50 amp range outlet of their own. This actually isn't all that hard to do if you have room in your breaker box for another circuit. You would need a breaker, wire of the appropriate gauge (don't know offhand, but can be looked up or asked at supplier), and a range outlet. Add to that the minor supplies - box fitting for the breaker box, staples or clamps for the wire, and it all is pretty cheap. If your breaker box is full, you'l need to run a sub-feed from the main bus to a second box for the breaker, a more difficult proposition, but still not that difficult. But of course you need to know what you're doing so as not to electrocute yourself or burn the house down. I'm not actually advocating that you do this work yourself. If you have to ask here, you probably are not ready to take it on. But if you are serious about getting into welding, and have a reasonable work space in which to do it, consider calling an electrician to see how much it would cost to wire in a dedicated welder outlet. I doubt it would be all that expensive, and if done right it will make all the difference in your ability to work. Put it near a garage door or other exit, so that you can weld either outdoors or with the door open. When at all possible, put the outlet in a position where you will not need to use an extension or a long cord on the welder itself.