Udyr used to be my main season 2/3. To answer your question succinctly, no, Udyr does not get a lot of kills or even assists, due to both of his currently viable playstyles. I'll elaborate below.
The fact is, Udyr gets outmatched in this meta because he has no efficient gapcloser. His bear stance doesn't do quite enough in most cases. Basic wards are usually counter enough against him, and regardless of wards, he's not useful at all in teamfights where the enemy team can spare even a little CC against him. Pretty much the only viable way to build him as a teamfighter beyond low-elo play is full tank, as his turtle stance gives you a good 200-300 hp shield every few seconds. For this, you want 
for engage, and 
for damage/scaling.
If you are so determined, however, Udyr has another playstyle, based on the fact that he excels at farming, objective control (dragon, for example), and splitpushing. The more resources you can force the enemy to divert to chasing you or keeping you off of objectives, the better you're playing as Udyr. This is also known as the Trick2G method, which, although probably very annoying and painful for your teammates, can work very well! The trick is to make sure your team can avoid being engaged on while you splitpush.
For this build, I recommend some damage (
, 
, maybe the new 
?) for two reasons: damage to objectives, and 1v1 potential. If you're splitpushing, you'll want to be able to kill any one enemy champion who comes your way. (If more than one comes your way, you run, trying to keep them on you for as long as you can. In this time, your team should be focusing on a different objective or killing the remaining 3 enemies).
I also recommend armor (
, 
, maybe 
though it's a cheap alternative) to reduce damage done to you by towers, in case you need to take aggro.
Always remember your boots (
) or 
are probably best unless you want to really run fast, in which case I recommend 
) and get alacrity on them.
Early game, clear camps. Do an early dragon if you can (make sure it's not warded). Really control those objectives. Your best bet to help teammates isn't ganking, but counterganking; try to figure out where the enemy jungler is, and be there to stop them after they try to go in. When you're just hanging out, waiting for fights, you poop on most enemy junglers in 1 v 1 if you can get in range, so feel free to walk into their jungle if their laners are busy.
Stances...You max your damage stance (either tiger or phoenix) first. If you're tankdyr, Turtle is second. If you're more damage, bear is second. The only time I don't recommend this is when you're going for hyperclear mode, in which you never leave your jungle; for that, max both damage stances first and ignore turtle. I usually prefer turtle stance over having both damage stances, though, so typically, pick the damage stance you like and let the other one chill until your last three levels.
Mid-game, still watch dragons, still farm, but you can begin splitting in other lanes, assuming your team can handle it.
Late game, it's all about towers and baron/dragon. Don't worry about clearing jungle unless there's nothing else to do (though at this point, you should be clearing enemy jungle camps and keeping waves pushed). Attack those towers. Get inhibitors. Make the other team panic and dance around. You can probably tank a few tower shots in exchange for dealing damage to the tower, so figure out your limits.
So yeah. That's a fairly comprehensive outline of 
. Hope it helps. If you want to do the whole Trick2G thing, I recommend finding some of his Udyr videos on youtube (I think he uploaded a couple for patch 5.8, so those'll probably be most relevant to you.) Ultimately, enjoy Udyr; he's one of the most versatile champions in terms of build paths in the game, and can really excel if played right.
