Booju, what sort of bird photography are you talking about - perched or in flight? How big, how fidgetty and how far away are the birds? If you want ultimate sharpness then you need....
- accurate focus
- sufficient depth of field
- fast enough shutter to negate subject movement
- fast enough shutter, or sufficient stability, to prevent camera shake
- sufficient contrat in the scene - the right quality of light and atmosphere
- enough optical magnification to make the bird a meaningful size in the frame
If your bird is perched then a tripod seems to me like a good plan. Mirror lockup can be used if you can aim where the bird is and then lock everything down, hoping the bird does not move away before you are ready to release the shutter.
Little jittery birds need high shutter speeds, as do birds in flight. Big birds may need plenty of DOF. Lots of DOF and high shutter speeds need good light and/or a high ISO. If the birds are moving (in flight) then your tracking skills are paramount, as is good AF performance from your camera.
You also need sufficient optical magnification to make the bird meaningfully big in the frame. If your bird is a little dot hidden somewhere in the frame and you need to crop heavily then your sharpness and IQ will fall apart.
Don't forget that the very best bird pictures you see will probably have had very careful post processing applied, to sharpen the details of the bird perfectly, while leaving the background nicely out of focus. There may well be tweaks to colour and curves to bring out the very best in the bird as well. It is worth shooting raw so that you have the best image data possible from which to create your masterpieces.
If I'm shooting perched birds in the back garden then I'll often use a tipod but not mirror lockup or a remote release. If I'm shooting birds in flight then it's always handheld for me. I've never tried it but I just don't think it would be very easy to track birds, at least at moderatey close distances - say <30m - with a tripod. You just wouldn't have the freedom of movement to respond quickly to random flight patterns. Maybe a big, slow, majestic bird like a swan would be OK, but not a hawk or owl, for example. Most of my bird shots are with my 100-400, at both ends of the zoom range. I like to try to keep shutter speed above 1/500 (preferably more like 1/1000-1/2000 if the light permits) and I normally do use IS. Even perched birds can go blurry at around 1/250, if they are nervous fidgets.
Can you clarify what sort of shot you are wanting to improve? Can you show us some examples, with EXIF intact, and then maybe we can make suggestions as to the best approach for those photographs.