DON'T GIVE UP!!!!!!!!!!!! You can get rid of the smell, it just won't happen over night.
Anywhere on the inside of it where it won't hurt the finish, use bleach water and make it fairly strong. On the outside use Murphy's oil soap, it is an excellent wood cleaner. Pull out ALL drawers and wash down the inside of the cabinet of the dresser too. Don't leave one inch of the dresser uncleaned.
Also, once done with the strong cleaning, use Febreeze. You may have to spray it for a few days, but it does wonders for knocking out that kind of smell.
After you scrub it down with bleach and Murphy's Oil Soap, it would be great if you could leave it set outside for a day or so. If you live anywhere near where I do though, at this time that can't happen since there is mounds of snow everywhere.
Maybe you could at least put it in your garage and leave the garage door open for a day or two to help air it out.
Scrubbing it well, and if possible leaving it set outside will do wonders.
Don't give up.