You say the balsa is covered, but how well? Algae needs light, as does pondlife. Don't panic too much about the wrigglers, they are as likely to be midges or gnats.

I suspect the requirement of a filter when using algicide is to filter out the algae. It is possible to buy small circulation pumps and filters, but I don't know where.

If there is a lot of muck etc. suspended in the water you might want to try liming it. You can buy a bag of cal from the builders merchants - it is large white crystals - not the stuff that looks like cement.  see: about lime.... But remember to wear eye protection and gloves - this stuff will boil water and a speck of it in your eye will boil your eye.

I agree, though, with Nigel that you should (eventually) drain and thoroughly clean the balsa before refilling it. It is possible, and cheap, to dose with household bleach, but you have to buy the one that says it's suitable for sterilizing water - if it says on the label somewhere "no apta para la desinfección de agua de bebida" then it's the wrong one (translated: not appropriate for disinfection of drinking water). I think it just means it's perfumed, so look for an unperfumed one. As for the dose, if you want to go this route, let me know and I'll dig out the gen. Certainly, you will have much better control of the chlorine content this way. Swimming pool levels are too high, really.

As a footnote, you don't know for sure where your water is coming from or what other source residues there are in the tanker, so it might already be heavily loaded with incipient algae and pondlife. The guys that deliver water mostly deliver to farms where water quality is not an issue.