Sounds like it could be a couple of things:
Cable needs to be lubed
brakes adjusted too tight
kink in the cable housing
bad/worn out/broken brake shoes
dirty/dusty brake pads
A honda dealer might have parts, but some of them are a pain about even looking for them- do some internet research and see if you can find the part #'s before you call or go to a dealer.
Watch the brakes when you pull the handle, does the cable seem to be binding up at all? Does it snap back cleanly when you release the handle? If so, take the cable off and lube it (hang it up, put the lube in and let it work all the way down the length of the cable),
How much slack is there in the handle? Do the brakes work immediately after pulling it, or not until halfway or all the way down? there are adjusters at the handle and on the rear brake, adjust them so that the brakes start to engage about 3/4" from the top of the handle.
If that doesn't help, the problem is probably in the brake shoes. There may just be dust buildup that's making them squeak, or they may be worn out and rubbing on metal. Pop them off and have a look.
A new set of brake shoes will probably run you around $20 or so, a rear brake cable around $10 or so.