I am going to disappoint you, unfortunately, as what you describe is not a problem that could be solved by simple stroller cleaning and maintenance (even though, cleaning and maintaining your wheels and other parts cannot hurt). Overall, this problem happens with cheaper strollers with wheels a lot.
You cannot really repair it as it is an internal looseness caused by a weak material. Apart from getting a new pram or frame, you can only fix the wheels in the locked position, so they wouldn't rotate at all, and push it a bit like a traditional, fixed-wheels stroller. That is the only thing that worked for moms overall, of course, not really making the turning easy, but at least a bit of help...
I am sorry. Try, perhaps, ask the seller about warranty or replacements chassis.