Bigger than that for koi - 10 gallons+10 per fish is for fancy goldfish. Common/comet/shubunkin goldfish need more, and koi need vastly more. A full grown koi from what I've read is between 100 and 300 gallons of pond stock depending on who you ask, and at their adult size, they'd take an aquarium almost as wide as my 55 gallon is long to turn around in.
Return the fish - they're very long lived (it's not unreasonable to expect a healthy koi to outlive its owner), but unless you've got a pond ready for them in a few months, you don't have nearly enough space for one, let alone six koi. Do a fishless cycle and either get small tropicals or one, MAYBE two fancy goldfish.
The cloudiness in the water is a bacterial bloom, which as jglover says is usually from ammonia in the water. Yellow is from fish waste, as well. The bloom itself is harmless, but the conditions that cause it usually aren't. The brown sludge in your filter is the bacteria that process ammonia. Over time it can get quite thick - I only recently noticed that the filter media in my mature tank is much heavier than the media in a new filter.