ENGLISH sparrows are considered a nuisance and therefore legal to shoot, if I'm not mistaken - you have to carefully identify them before shooting - study pictures on the net. As for other birds, be careful - there's something like 800 or 900 species on the Migratory Bird Treaty Act list, including a ton of common species which you may not think are migratory, including the great-tailed grackle, which are more common around here than blades of grass - massive infestation.
http://www.avianweb.com/sparrows.htm
http://migratorybirds.fws.gov/intrnltr/mbta/mbtandx.html#a
If you kill a bird on that list accidentally, shoot shovel and shut up, as they say. Notably, English Sparrows and European Starlings are not on the list, but other "infestatory" species are.
Oh, my $55 from Academy, Crosman RM377 is the best value in airguns I've ever bought - it's a break barrel springer, advertised at 825 fps in .177 - with Lynx rings and a Bushnell Banner 4-12x40mm AO on it, I am deadly accurate with RWS Superdomes. More accurate than super colibris out of a .22, almost as quiet, and correct, you don't need or want the overpenetration of a magnum (900+ fps) airgun when shooting little birds. 600-700 is ideal, but 800 will work, and so will 500.
Right, owls and snakes don't work. If you move them every week, they'll work for awhile, but eventually will quit working. Things that move with the wind eventually quit working as well in my experience. Best remedy is shooting them - some are good eatin' (feral rock doves).