When I first started fish in my "water feature" pond I had lots of string algae too. I had a bio-filter which kept the water clean. I added lilies and other water plants...but the goldfish were small. This pond sits in full afternoon sun. Locally the pond shop told me I had too many fish for the bio-filter, add some surface plants, and to stop feeding the fish too much plus some shade when it's too hot would help.
I did as they suggested - stop feeding the fishies so much, added floating water plans and parrot's feather and anarcris (sp), put up an umbrella. The pond lived very well for a few years until I stupidly took all the plants out so the fishies would have more room. The water parameters went through the roof, almost lost the koi I've raised for over 5 years plus some new ones and the last 3 original goldies.
Now after three weeks of worry and lots of partial water changes and prayers for warmer weather the water has bounced back. Also I put plants back into the pond...a bog like corner for many waterplants and a few floating pots for hyacinths, floaters, parrot's feather, anarcis, and watercress and the likes that don't need soil.
It may take some time to correct the balance but once you get it it is so worth it. I can see my fishies and I restrain myself from feeding them so much. In fact I hand feed them now.
Good Luck to you!