Is it possible to pet/groom birds?
Birds do groom, but not like mammals do. People tend to call their grooming behavior preening. Preening removes dirt and parasites, arranges the feathers nicely, and distributes oils over the feather (very important for waterfowl.) 

To answer your question better, we need to look at the specific species. Lots of birds preen each other socially, so if you wanted to pet a bird (in a way it likes) it's good to know how the species behaves. 

You mention crows and owls. Crows are social so they may preen each other; they're also sophisticated (cultural) so it's hard to generalize. A 'bird nerd' on YouTube shows convincing footage of such behavior. I think family groups of crows preen each other, but I don't have a source. 

Owls tend to be solitary and would not understand preening behavior from a human. A social species of owl might preen; I don't know. Of course, if you just go ahead and pet your owl like a dog, it may appear to like it. It's hard to say if it does like it...it's easy to anthropomorphize a bird with binocular vision!