Another point to mention is that if you have a bad smelling case, you should KILL IT WITH FIRE!!!!1111one
Erm. If you put a completely redone saxophone in a smelly case, the sax will start to smell again. The reverse is also true: put a smelly sax into a new case, the case will start to smell.
My "kill it with fire" comment is actually quite true. It is possible to reduce the smell using a whole variety of different techniques on both a case and the horn, but none of them will completely work until you remove anything that's not metal (well, porous) from the case and the horn. Then you need to get the horn cleaned. However, if you've got a good playing horn (it sounds like you do), you might want to try an ozone machine, coffee grounds, activated charcoal or any of the other tips and be content with the smell. And clean out the inside of the horn with a swab. There's a tech out this way that dunks disassembled horns in Simple Green. I've used rubbing alcohol. I'm also not a instrument tech.
Having the horn completely repadded, all new corks and all new felts is kinda pricey -- and will be more if you have big ol' dents or bad repairs that need to be cleaned up. A case won't be expensive, unless you want something like a flight case. You could probably do well with most used cases, even.
Oh. One other thing if you're wanting to try disassembling the horn: those are called "needle springs" for a reason. Make sure your shots are up to date.
One other thing on cleaning: if you decide to polish the horn, use a non-abrasive, non-tarnishing polish that's for the metal your horn is plated with -- most of the Lyon & Healy horns I've seen are silver plate -- and be gentle. It's easy to bend stuff.