Sounds like you need yourself some brushes. Usually PetsMart or whatever LFS
near you will carry a set of brushes designed for hoses - Fluval makes them or Eheim makes them, probably others - any of them will work. I use a scrub pad on the canister itself, and you could probably use an extremely weak bleach solution on that.
I'd hesitate to use bleach on the vinyl tubing, but I have coiled the tubes into a wide tub and poured water just off the boil into it, so the tubes soak in extremely hot water, rendering them soft for a while, but dislodging a lot of the gunk. This stuff slows the flow and should be dealt with periodically but is otherwise likely not dangerous. Brushes make this process a lot easier.
One trick with the brushes for hoses longer than the handle is to tie a long piece of fishing line or even string to the end of the brush with a fishing weight that will fit very loosely inside the tubing. Drop that in first and shove the brush down. When you run out of handle the fishing weight should be dangling out the other end of the hose. Give that a pull and that will run the brush through the entire hose.
Lordy my posts are long - I need to get out more...