Getting the tubing & pump wet will help to soften the algae; it may take a little soaking. A small weight, like a nail, on a string longer than the tubing with a piece of cloth attached to the other end will work for tubing cleaning. Feed the end with the nail through, and pull through the cloth.
For disinfecting anything except for the fish themselves I use plain bleach, 1 part bleach to 20 parts water. Rinse really good afterwards, I double up on dechlor after using bleach on tanks or filters, it neutralizes chlorine, this includes chlorine bleach.