Buttons can all be remapped using the menu system. You can remap buttons on a per-game basis, or in your case, system wide, by going to the configuration-configure controllers menu.
By default, the button mapping should not be nearly as wonky as you're describing. I'd suggest completely re-installing the emulator (this includes deleting the stuff off E:\TDATA E:\UDATA and e:\saves)
While perhaps a bit out-dated and not specific to the neogenesis emulator,
this documentation may help if you need to actually remap the buttons to make it work.