Note that all these gates are not reversible. As such, it is not possible to implement these "in place". However, you can using the well-known scheme:
By definition, the Toffoli gate is exactly the one you're looking for. So, you can't use less than 6 CNOT to implement it exactly. Note that there are some decomposition which use only 3 CNOT at the cost of a relative phase. Thus, if you plan on uncomputing this gate at some point, you can afford only using 3 CNOTs.
It is quite easy to implement an AND Gate from a NAND one: simply apply an $X$ gate on the output. Since the optimal decomposition of the AND Gate is known (it's simply a Toffoli), it's not possible to do better for implementing the NAND Gate.
Once again, it's quite easy to implement an AND Gate from an OR one: simply apply $X$ gates on the controls qubits before and after the OR Gate. As such, this not only shows that you can't implement an OR gate using less than 6 CNOTs, it also gives you the optimal decomposition.
Finally, you ca implement an OR gate from a NOR one by applying an $X$ gate on the target qubit. This also implies that this gate cannot be implemented using less than 6 CNOTs.
Since all these gates can be built from one to another without using additional CNOTs, their optimal decomposition in terms of CNOTs gates is the same. Since we happen to know that the optimal decomposition for the Toffoli gate uses 6 CNOTs, you cannot find an implementation that uses less than 6 CNOTs, as long as you want to implement them perfectly. You can use as less as 3 CNOTs if you allow relative phases though, which is still a 2x improvement.