I have issues with birds in my house too. They come down behind the flue or something (roofer can't find out where they are getting in). They go behind the fireplace enclosure and come out in the basement where the opening is for all the ductwork to go up to the other floors.
About 6 times a year I get sparrows in the house and the cats absolutely go nuts trying to catch them. Then I come home and grab the butterfly net and half the time I can get them that way. If I can get them out of the basement, its a straight shot to the back door and out they go.
Cats usually sleep well after chasing them all day while I'm gone.
I'm surprised the hummingbird is ok.