I guess boiling is not an option? Honestly, I'd just get some pool algaecide and put that in. I use that on my broms and it's fine. The dosage is the hard part.

How you keeping the mosquito's out of it?

Are you keeping the lids on? If it's algae and you block the light you should be ok. This is assuming you don't want them open constantly to catch more rain.

You can filter the water using at least two layers of old blankets or cotton shirts. As Mike says, keeping the water in the dark will prevent.

Tomas