Check to make sure your loads are balanced on each phase of your generator. If you've got the meters on the transfer switch start the microwave while the oil burner is running (they may both be on the same phase and not enough load on the other side) and see how out of whack it gets.
As far as the boiler contol I had the same issue with my Tekmar 260 not working on the old genset. Check your voltage at the control to see if its high enough (while you're at it check it at an outlet) to see if its just too low. I was getting 105vac (barely enough) at the control but it would drop whenever the burner would kick on and that would shut down the control again. Click, click over and over. You've got a larger genset with plenty of pwer so that may not be it. Are you trying to use the idle control per chance?
As far as the boiler contol I had the same issue with my Tekmar 260 not working on the old genset. Check your voltage at the control to see if its high enough (while you're at it check it at an outlet) to see if its just too low. I was getting 105vac (barely enough) at the control but it would drop whenever the burner would kick on and that would shut down the control again. Click, click over and over. You've got a larger genset with plenty of pwer so that may not be it. Are you trying to use the idle control per chance?