If your ammonia and nitrite were through the roof you need to do a lot of large water changes to get them down to zero and then as many water changes as often as necessary to keep them there.
What was the ammonia remover you used? It is usually better to do the water changes than add chemicals.
Plecs are poo machines, as you have discovered. They will not be helping the water conditions. With four of them in there I'm not surprised you are having trouble. I'm afraid there are no plecs suitable for a 64 litre tank. The smallest plec commonly available is the bristlenose, but even that needs a bigger tank. At the other end of the scale are common plecs and gibbiceps (sailfin) plecs which grow to well over a foot long, and probably longer than your tank.
Quite honestly, I'd see if any shops would take the plecs off your hands. Even if they do they most likely won't give you anything for them, or maybe a credit nore if you are lucky.
If you can rehome them, the neons and harlequins would be fine, though you'd need to get more eventually - they should be in shoals of at least 6 each. But I would wait before gettting more until you know that your ammonia and nitrite are staying at zero as adding more fish just yet will make the situation worse.
You say you had the water tested - you really need to buy your own liquid reagent based testers (not strips) because you need to be testing the water at least twice a day for a while, and doing a water change every time you see a reading for ammonia and/or nitrite above zero. This sounds like a lot of work but you will get there, especially if you rehome the plecs.
In between water changes, can I suggest you read
this as it explains in more detail what you need to do to keep your fish alive and healthy.
Don't worry about the cloudy water for now. It's either sediment from the gravel/sand/ whatever you have on the bottom of the tank, or more likely a bacterial bloom - but these are not the same bacteria as grow in the filter. You mention moving the fish into your home and into a 64 litre tank. Is the tank new? If it is, that's what's causing the bloom, and if the filter is also new, that's what is causing your ammonia and nitrite problems.
Ignore what shops may tell you about not doing water changes or adding chemicals. The best thing you can do for your fish is water changes and add nothing but dechlorinator to the new water.
Any more questions, just ask.