Furniture oil vs wax?

We have inherited several old pieces of furniture. They are about 150 yrs. old. I have been oiling them over the years since we have a very dry house in the winter. I oil (using old english lemon oil) them no more the 2x a yr. Now someone said to me that I should be waxing them and stripping them with mineral spirits. They are in good condition and we use them. If you strip them wouldn't you take off the finish and given their age - should I even bother? Their color hasn't changed at all since we've had them although I suspect that they were probably lighter at one point. I'm not even sure what kind of wood they are, something from VT I guess.