Kind of X constructions are so commonly misused that the formal use I am going to describe might be labelled eccentric by a dogmatic descriptivist; so I’ll preface my remarks by saying that in conversation and informal use you may use any of your four variants, and no one will even notice, much less object.
First, kind vs kinds: let’s come at this from the side. Labrador is a breed of dog, and spaniel is another breed of dog. Dog [singular] is what logicians call the ‘genus’: when we invert the noun phrase we say these are two dog breeds, not ✲dogs breeds; and we likewise say, in formal use, that “Labrador and spaniel are two breeds of dog [singular]”.
In the same way, if X is one kind of problem, and Y is another, we have defined two kinds [plural] of problem (singular).
When we use this construction in a sentence, however, things get a little tricky. The formally correct way of expressing what you’re after is
These kinds of problem are to be avoided.
But at this point a subtle difficulty intrudes. What you want to avoid isn’t really the kinds—it’s the problems. In ordinary conversation, there is very strong pressure to say problems, in the plural, because that’s what you really mean. And in conversation, that’s OK: you cast both nouns in the plural, and it’s perfectly acceptable:
?These kinds of problems are to be avoided.
(Note, however, that you never say ✲These kind [singular] of problem; that’s a mismatch which makes neither semantic nor grammatical sense.)
But in formal use, this won’t do; you need to keep problem in the singular where it expresses the ‘genus’. So what you do is rewrite, ‘fronting’ problems to give it its proper status as the topic of your sentence, and postposing these kinds to make it clear that this is a qualification of problems:
Problems of these kinds are to be avoided.