Every sink in our apartment is giving the most dramatic odor. I've tried many chemicals down the drains (clr, bleach, etc), and I have tried cleaning underneath, checking for wet/damp areas (which there are none), looking for mold ~ nothing.

We've been here for only 2 months and I had hoped that it would go away once we got unpacked.

I'm ready to call the landlord and ask them to battle it - but I anticipate them saying that there's nothing they can do and I'd like to be prepared with some suggestions?

It's killer though. I grew up in the country - so I've smelled dead animal and this IS WORSE. Seriously- and it's in EVERY single bathroom and the kitchen. There's no rhyme or reason to it - it's 24/7 and never lets up.
Help!

Most bad smells in tubs, lavatories and showers are caused by rotting hair matted with grease from the soap and from rotting food in kitchen disposals try this for the smell. Tonight before bed time take a 1/2 gallon of bleach and pour it down in each drain and let set over night. Next morning, (and this is important) flush out the drain with two large pans of boiling water to loosen the grease and flush the mess out. The bleach will make the hair slippery and began to dissolve it and the hot water will melt the grease and flush the mess away.
Also, pull the lavatory stopper and look down the drain. About 4 inches down you'll see a small rod sticking out. Fish out any hair that's caught there and do the same thing to the lavatory if you detect any odor. This should make your drains smell better. With all chemicals used in drain cleaning proper ventilation should be observed.