I began noticing a smell in our 1st floor downstairs sink beginning in the spring, probably around April. It would occur immediately after running the water in the sink after being unused for awhile. Because we had a new roof put on last fall, I started wondering whether there was an issue with a vent caused by the roofers. Well, I finally went up to the roof to check and found that one of the vents, 3" PVC, was angled at about 20 degrees from vertical. Looking down with a flashlight, I saw that it wasn't centered over the lower pipe and there appears to be a bend where it joins. I could only see about a 1" wide section of the lower pipe opening. I poked some wire down and it didn't seem to be obstructed. I can't tell, however, if there's a constriction.

First of all, I've never seen a vent at an angle like this. Is this as hokey as it seems?

Secondly, is this the cause of my problem? I'm waiting to see if poking the wire through the opening has cleared an obstruction and solved the issue.

It is NOT, nor was it ever, the problem or the solution. More than likely the overflow passage in the sink is "fouled" with debris, and when you run the water it pushes air through the passage, carrying the odor out with it into the room.