I'd get a bag of daphnia or water fleas from an aquatic store and add them. They eat greenwater algae and bacteria as long as they don't get eaten by fish or damaged by pumps. They breed quite quickly but they'll take a bit of time to conquer it - perhaps a few weeks. The more you add, the faster they'll tackle the murk. As with most wildlife gardening, it's the base of your trophic pyramid that's the most vital.
Watercress is also a fantastic native biological control which will grow from cuttings, or more usefully, supermarket bunches. Remember that submerged plants won't grow well in murky water due to low light levels, so as has been said marginal or tender floating plants like water hyacinth are more useful until the water clears.