To echo John G's comments. The best way to improve your bird photos is to get as close as you possibly can. Now, that may sound rather obvious, but there are a few tricks to help you get there.
One is to set up a bird feeder, preferably one that accepts sun flower seeds. Reason being, you'll attract a wider variety of birds.
I have a feeder set up directly outside the window in my home office. The feeder is literally 4ft away from my lens/camera mounted on a tripod. I shoot thru my storm window (which I wash almost daily). I use a black foam board on each side of the window to eliminate glare.
By the way, you'll get lots of Black Capped Chickadees and Tufted Titmouse which are difficult to capture as they are so fidgety. But, the Cardinals, goldfinches and house finches are more predictable and will allow enough time for you to snap a picture.
To make the photos more natural looking, I cut holly branches and mount them to a little board on the other side of the window. Many of the birds alight on the branch to wait their turn. Call me crazy, but this set up works.
Shutter speeds are 1/800 sec minimum with 1/1000sec a better choice.
Using this kind of set up, you can actually manually focus as the birds are in a predictable location, so you can focus the camera to one spot. By using manual focus, you can speed up the shutter.
Be prepared for failure, as these critters are fast. But, with practice you'll increase you're success rate to 10-15% or better.
A couple of pics taken using this set up. To be fair, I used the E-510 and 50-200mm Olympus lens. However, you can get very close to these results with your set up provided, you try manual focus which should eliminate shutter lag.