These materials should have good weldability. As always with stainless, keep it clean.
I have a datasheet from Carpenter Technology for 21 Cr - 6 Ni - 9 Mn, which is their version of Nitronic 40. (www.cartech.com) The datasheet recommends using 309 if the mechanical properties of the Nitronic 40 are not required for the weld. 309 is acceptable for joining both 304 and Nitronic individually, and therefore good for joining them together. I think that 308 would be OK also based on the constitution diagrams (WRC 1992 & Schaeffler Diagram). The ASM Handbook volume 6 "Welding and Brazing" has good expainations on how to use the consitutution diagrams. The AWS handbooks also have some info on how to used consitution diagrams. Does this joint have any special service requirements, such as magnetic permeability? If so you would have to consider using nickel based fillers which are completely non magnetic
You can use 308 for joining 304 to 310. This is listed in the welding and fabricating data book. Unfortuneately, I don't know who published this book since I only have pages copied out of it. Type 309 would also be acceptable.
Regards.