I saw a gull the other day who looked for all the world like he was doing a loop. Of course, doubtless the light was playing tricks on me.
Have any birds ever been observed doing loops, barrel rolls, or other aerobatic feats?
Anecdotally, my father told me stories of gulls following his hang glider and flying into the vortices of the wing which caused them to flip or tumble away. They seemed to be doing it for fun.
I’ve seen birds do barrel rolls. Usually when they are fighting or courting another bird (e.g. they fly below it then roll belly-up to grab with claws or something then complete the roll to right-side-up).
As for loops not sure they can and if they can why it would occur to them to try.
Here are some stunt ducks. 
I have seen ravens do some impressive aerobatics (observed both from the ground and from a sailplane). They seem to favor “half-rolls” where they briefly roll upside-down, then reverse the roll to finish rightside-up. But they will occasionally go all the way around in the same direction.
I haven’t seen any genuine loops, but have seen some complicated sequences that make it clear a loop would be no problem.
I’ll raise you a goose…
Swallows are particularly nimble in the air. I don’t know about the specific maneuvers in the OP, but I wouldn’t be surprised to see them, particularly if the moves come about from chasing a meal.
I’ve seen a fox do a barrel roll.
Hummingbirds do both loops and rolls as part of their territorial/mating displays.
And on the homefront… I’ve had pet parrots do “aileron rolls” (they don’t have ailerons, but it’s the same result), stalls, slowflight, spins, and immelmans, among other aerobatics.
Hummingbirds are the most adept flyers, but most other birds can perform a respectable airshow routine when they want to.
When hunting geese I have seen many tumble in the air. They were dropping into a refuge just out of shotgun range and it seemed that they were just going to fast and the wings would fold and they would tumble.
At 4pm (close of shooting hours) they would fly over in baseball range:dubious:
The most impressive flying I’ve seen yet has been a magpie - they use those long wing and tail feathers to incredible advantage. They use them closer to the ground, though, for astounding take-offs and landings - not sure about loop-de-loops.
My wife took a picture of two hummingbirds fighting over our feeder. One of them was hovering upside down, with his beak pointing straight up at the hummingbird that was over him in the air.
I once saw a male scissortail flycatcher land on the back of a redtail hawk while it was flying, and commence to peck and scratch bloody hell out of the back of the much larger bird. I really, really wish I had had a video camera on that. I had been watching Momma scissortail harrassing the redtail, and the redtail was flying away, in my general direction. Then papa came flying in on a beeline and landed right on his back, right in front of me, right as the hawk was passing. Way cool. Scissortail flycatchers are some really cool flyers. They can make a ninety degree turn at incredible speed. But I don’t think I ever saw one complete a barrel roll.
One of the falcons about 3/4s of the way through this does a 180 degree snap roll. They replay the maneuver in slow motion, but I had to slow that down to 20% to be sure what it was doing. From what I have seen, falcons also seem to prefer half rolls, but I bet if you slow this down and watch the whole thing, there has to be some full rolls in there somewhere.
There’s also one about 5 second after the start.