Birds often get into the Dryer Vent and nest. Sometimes they wander down the wrong way and end up in your dryer. This happened to me last summer.
First step, check your outside vent, and pull out any nest or other nesting like material. You may need a long stick to reach as far in as you can and pull stuff out. I used a broom handle. Just be careful not to push the material built up back further. Then, buy a latchable cover from Lowes or similar, and install it. Make sure no other birds or rodents can get in. (It's probably a bird)
Next, pull your dryer out, and clean out the vent from the back. There will probably be a bird or two. In my case, they were both still alive, so the smell wasn't as bad as yours will probably be. Get the birds out, and wipe it out the best you can. It'll still smell awful. Get some bleach and mix it with water in a spray bottle. I think I used around 30% bleach / 70% water. Spray it down and let it sit for 30 minutes. Then wipe it out with a clean wet cloth, then a clean dry cloth.
I hope that fixes your problem!