How to get rid of the smell of spilled milk from the carpet

Sorry to hear about your stain, but here are two options.

Tea should be fairly easy to remove. You can try blotting it out with very hot water and an absorbent cloth, or borrow a carpet cleaning steam machine and give it a try. Another option would be to hire a commercial carpet cleaning service. I use this type of service all the time in the apartments I manage. In this area it only costs me about $80 per room and the results are amazing. If you talk with a cleaning service, they can tell you if your stain can be removed before you hire them. Some will guarantee that the stain will be gone. This option is certainly a lot cheaper than paying to replace the entire carpet and padding. Good Luck.

I don't know how true it is but I've heard a few times that certain plants do a good job of removing VOCs from household air. You could try investigating this claim. Here's one page that mentions it.

http://www.thedailygreen.com/going-green/tips/best-plants-for-indoor-air-quality

My wife has trouble with a variety of VOCs. It might not be an option for you to store the carpet partially outstretched in your garage until most of the odour departs.