Welcome to the forum. These images show some of the problems of shooting small birds in big trees. - background branch clutter. Not to much you can do about it, except to watch for a few things that I like to call "sprouts" (others may have their own name for them). By these I mean branches sticking out of the top of the bird's head or its side, or coming into one part and exiting out another part of the body. Your first two show this type of a problem. There are probably only two ways that I know of to deal with them - 1) learn to use your cloning tools to your advantage, particularly things like content aware fill, or 2) wait patiently until the subject is not a victim of "sprouts".
The other thing that jumps out to me is that in each of your images, your subject is more or less in the centre of the image. This always produces a very static image. If possible, you can use the "rule of thirds" to place your subject, or just move it off centre. For example, in the first one, I might have moved the subject a bit to the left of centre, for the second one, I would have moved the subject, tree and all more to the right of centre, and for the third one, I might have, again, moved the subject a bit to the right of centre - this gives it more room to "hop" along the branch. This sort of positioning can give the viewer a sense of a more dynamic subject. Also, for the third one, I would have, somehow removed that curved bit of twig above its body as I find it very distracting.
The other thing that is important when photographing wildlife, is to make sure the eye, or eyes, are in focus and visible. You have managed to do this in the first and third image, but not so much in the second one.
I can't really comment on your post-processing, as I do not know what software you are using. Also, just out of curiosity, are you shooting raw?
Hope this helps.
WesternGuy