Actually they CAN loop. They just don't get much practice and it's odd to them.

Some years back there was an article in Model Builder about someone slope soaring when a hawk came over and started stooping (attack passing) the sloper. He did his darndest to get away including a bunch of manuevers. In one case the model did a 1/2roll and looped back. The hawk paused for a moment and then did the same thing. After a while the hawk lost instrest and left.

At my own power flying field one day I was watching a hawk thermalling for altitude (once a thermal flyer always a thermal flyer I guess ). Suddenly he dove aggresively and I thought he was either heading out or going after dinner. I was totally shocked when he nosed up to vertical in what looked like an attempted loop. He got up close to inverted and fell out of it with a huge raucous CAW. Now this REALLY got my attention and I called to a few others that were there. We all watched while it thermaled back up to height and did a second try. This time the dive was more than just a high speed cruise and when he nosed up there was enough speed to loop right over. But I guess it was too much work for his wings or something as he thermaled back up and left the area with a few lighter calls almost like he was saying "Nah-nah, I can do it too you turkeys!".

So while it's not common don't let anyone tell you that a hawk can't to stunts.

Sparrows and other small birds just flit about and bounce off the air. I've seen them do flicks and half loops and half rolls of all sorts.