First of all, make sure you're using the latest game version -
http://worms2d.info/Updates_(Worms_Armageddon) /
http://worms2d.info/files/WA_update-3.7.2.1_Installer.exe . What you say very much reminds me of certain old version problems.
Then make sure you set renderer to Direct3D 9, preferably the shader one. To get to those settings, launch W:A, then go to Main Menu -> Options (that one big button with question marks on it) -> Advanced (a black button at bottom-right corner, right above Exit), and from here check out the left column where it says Graphics. See the drop-down list and choose
Direct3D 9 (shader). That's what should work the best on most systems.
As Rabbit said, you can try to turn off vertical synchronization options, located at the same place where renderer settings are. I don't know how much noticeable the effect would be, but you can safely check it out for yourself - if anything goes worse, just turn them on back.