I doubt if it's the vent. It's made of 1-1/4" plastic pipe. Dirt or dust won't clog it and it's too small for anything to build a next in - maybe a spider could. We were having odor problems also. Here's my cover removed because someone insisted I go check it.
Look above at downtheroad's diagram. Right in the middle of it are two ASTVD vents. We have three of them and one of them was bad. I changed all three. In reading one of the vent mfg's web sites, they said they usually last ten years before they go bad. So Rather than playing guessing games as to which one was bad and then wondering when another would go bad, I changed all three. They are threaded, just unscrew them to remove them.
This is the sink that gave me a lot of problems. The vent was within a 1/4" of the sink bowl. I went to HD, Lowes, and a couple of plumbing stores. All they had were ones with larger diameters and therefore wouldn't fit. They fit on two of the sinks, but not the third one. It took a lot of driving around to find a small diameter one at an RV shop.
So find your vent valve(s), see if you have room for larger ones, take one off and take it with you to the store.
Bill
Nodwell RN110 out moose hunting. 4-53 Detroit, Clark 5 spd, 40" wide tracks, 10:00x20 tires, 16,000# capacity, 22,000# weight. You know the mud is getting deep when it's coming in the doors.