"In the last months" can be translated straightforwardly as
In den letzten Monaten.
For "in the last few months", would it be
In den letzten einigen Monaten
In den einigen letzten Monaten
or neither of those is correct?
Neither of those are correct; The few is already implied in "In den letzten Monaten" - you wouldn't say that if you actually meant many months. As fifaltra pointed out, you could add "paar" to make it more obvious.
"In den letzten Monaten" is fine, your other examples would be wrong.
"In letzter Zeit" can be used if the context is clear or not that important (e.g. "In letzter Zeit sind die Preise für Benzin gestiegen")
I would not use "paar", in my opinion it is slang in this context. At least i would not write it down that way, though i actually might say it.
You can also say "Während der letzten Monate" The exact translation would be 'during the last few months' and this does not mean the same as "In den letzten Monaten" - the difference is the same as in english.