50/50 mix of vinegar and hot water (don't worry about the water staying hot, it just seems to work faster when you start with hot water).
On the tank, if its not bad or too heavy, use a sponge to soak the coraline until it breaks down. If it is heavy, fill the tank with the vinegar/water and let it soak for a few hours (or days) untill the coraline breaks down.
If the pumps are submersable, throw them in a bucket with the same vinegar/water mix to soak. Plug them in to get all the internal parts clean (I do this with maxijets and mag pumps every 6 months for maintenance anyway). If you fill the tank due to heavy coraline coverage, throw the pumps in there and turn them on - this keeps the water moving and speeds the breakdown of coraline.
Once clean, rinse everything with RODI and towel dry.