I think you can improve your bird photography quite a bit without relying on post processing. Considering the images that you posted, at this point it really isn't about what you do in post.
I think it would help you greatly if you took more control of your shoots. By that I mean, instead of letting the existing conditions dictate how to shoot the birds, you can set things up in such a way as to gain more control of the elements in your photos:
- Get closer to the birds, or shoot with a longer lens. If you don't believe you can get much closer, I challenge you to just give it a try. Set up a blind that will completely conceal you. If you do, then you will be very surprised at how much you can close the distance and put more pixels on the birds. Even if all you have is a 70-200, you will still be able to get much, much closer than you are now.
- Choose what your background is. Don't just settle for whatever happens to be behind the birds - determine what will be behind them. Set your feeder up so that you can shoot in line with some nice green foliage. Or, lacking that, line the feeder up where there is a lot of open space behind it, so that background elements will be more effectively blurred out. If the birds are in shade, then make sure the background is as dark as possible. It may help to buy several yards of cloth material of a natural-looking color, and hang it up 20 or 30 feet behind the feeders, to ensure that you get a "clean" background. No matter how you solve your background troubles, just make sure that you are choosing the background, and not just "stuck" with whatever happens to be there.
- Camera position with regards to the angle to the subject. As another person already suggested, seldom can good results be obtained when shooting down on a bird. Try to have the camera on a level with them. This will normally result in a much more pleasing perspective.
- Don't be afraid of slow shutter speeds. Slow shutter speeds can be great, because they will allow you to shoot at much lower ISO and also use smaller apertures, such as f8, which will result in sharper, better resolved feather detail. Be sure to use a good sturdy tripod, and work on technique so that you can keep the camera solid and still. This will take some time, but is very well worth the effort. If I were you, at this time I would not hesitate to use shutter speeds down to 1/100th of a second. Then, after some weeks/months of practice, you should be able to get consistently brilliant results at 1/40th of a second, even with a very long lens. I do not recommend having the ISO any higher than 400.
"Your" and "you're" are different words with completely different meanings - please use the correct one.
"They're", "their", and "there" are different words with completely different meanings - please use the correct one.
"Fare" and "fair" are different words with completely different meanings - please use the correct one. The proper expression is "moot point", NOT "mute point".