I'll preface this with saying I'm a noob, I don't know what the correct names are for parts so bear with me.
I have a Trek Mountain bike, fiance has an older Schwinn Mountain bike. Over the winter we moved and we stupidly left our bikes outside at our new APT. So the chains and gears are rusted. The chains won't even bend. What's the best way to fix this, the chains(if I can get them off ) do I soak them in oil and take a wire brush to them or what? I've bought this other stuff called Naval Jelly Rust Remover, is this recommended? What about the rust on the 'gear wheel'?
Also, my back tire and 'gear housing' was stolen
How much am I looking at to get that replaced?

Your chains are shot. you can get them off (with a chain tool) and soak them in degreaser/solvent, clear off a lot of the junk, but the chains are probably rusted internally as well, and will never work again - you may get them to bend smoothly, but there will likely be a lot of "chain stretch" even if that happens and the chain will wear down the teeth on your chainrings and cogs.

You can buy a new SRAM PC-48 for around $15 - it's what I use on my commuter. Pay a bit more for nickel-plated chains that are more rustproof.

My advice would be to buy a chaintool that allows you to break the old chains to get them off the bikes. Buy a new chain, use the chaintool to shorten it to the same number of links as the chain it's replacing, and attach the new chain (SRAM chains have a masterlink that you can connect and disconnect wihtout a chain tool from that point on out - but you'd need a chain tool to shorten the chain in initially).

Sitting out in the winter is also bad for your frame, if the bikes are steel/cromoly. At the very least, remove the seatposts, turn the bike around to try to drain any water. Then run a fan near it, blowing inside the frame, to try to dry it out. Most frames that "rust out" and fail do so from the inside.

The next step would be to coat the inside of the frame with Weigel's Frame Saver or comparable product. You may or may not want to go there - it's a fair bit of work, especially if you don't have proper tools, or experience, to remove the bottom bracket and the fork.

Chain, you might as well replace. A new chain can be had for like $15 or less. On the "gear wheel" (I believe you're talking about the front gear(s), referred to as chainrings), easiest thing is probably to (once you get the chain off) spin the pedals by hand while holding a wire brush against the chainring. I'd use some sort of soapy water too just to help wash away any gunk rather than flinging it about into your eyes etc.

Back tire, I assume you mean the whole wheel? With the rear gears and all? Depends a LOT on the quality. If this is a nice bike it's probably worth replacing the wheel. If this was a sub-hundred-dollar walmart special, you might as well buy a new bike unless you can find a used rear wheel somewhere.

[edit] Oh as far as removing the chain, since it's trash anyway, just use bolt cutters. Piece o cake.

Thanks.
Looks like the bikes are going to have to go to a repair shop
Any recommendations for shops in Chicago?

Yes the whole wheel and the rear gears. The bike is not a walmart special , it's a 2002 Trek middle of the line mountain bike, it was on sale for around $300. Roughly how much will the rear gears cost?

You're looking at probably over $100 to replace the rear wheel, gears, and tire. Your cheapest bet is to get something on eBay (where there's a good chance you can get all three at once), if you know what you're looking for. Biggest issue will be making sure you have the right number of gears (probably 7 or 8 on that bike). 7- and 8-speed freehubs have different width. 8- and 9-speed gear clusters fit on the same freehubs.

I searched eBay for 7-speed rear 26" wheels, and this is the only viable (in your price range) one that I found. Lots more high-end stuff. You'd need to buy a tire/tube and cassette sprockets to go with this.
https://cgi.ebay.com/ws/eBayISAPI.dll...tem=7233373036

Thanks for looking that up. Going to call the shop I bought the bike from and see what they say first. Might just end up getting a new bike, they have this 2006 for $309

https://www.villagecycle.com/images/t...N/3700_RED.jpg

Yeah, it might be worth your while just to get a new bike, at this price-point.
I'd say that unless you'll be riding trails, no point in getting a mountain bike with front shock, though.

Good point about the shocks because I do only intend to ride in the city, mainly just for some exercise.
This is actually the bike I have, it's only $169 thru the 17th. With you saying it's going to cost $100 or more to fix mine, probably makes the most sense, not to mention the hassle of the whole thing, to just go with this one again.

https://www.villagecycle.com/02_800sport.asp

Can I get any $ for the frame on my old bike?

I've been quite surprised at how durable cro-mo bikes can be. I've rescued several from years of outdoor abuse and found only surface rust that came off easily with steel wool. The chain certainly needs replacing but cogs and chainrings and rims and such are possibly just a quick polish away form being fine. I just recently restored a tandem whose fenders looked to be solid rust. I rubbed a small section just on a whim and it magically became shiny chrome again. Try a good cleaning first.

We're going to do that with my fiances bike.
as timcupery said:

I just called Village Cycle, quoted me at $175

Looks like it's time to go shopping. the link I gave above for the 2002's she said they only have woman's frames for that. I see your in Naperville, any other shops in the city you can recommend? There's one on Broadway near Belmont I know of.

Yeah, just buy the new one then. You can probably sell the old bike for parts, although they won't bring much... If there's a bicycle co-op in your area, you could drop it off there...

dont use naval jelly as it is corrosive to skin. wear chem gloves.