If it is a local move just to a larger tank at the same location.?? Also is the 130 already cycled etc??
If so be sure water in the new and old are at the same temperature , salinity and PH.
The described corals are all pretty hardy and should do fine. Just remember the normal cautions with handling Zoa's if pulling them off of rocks or close contact is necessary..The mushrooms and Zoa's even with tearing apart fron rock to rock if this happens will not hurt them. The Xinia pretty much the same , it is a hardier cridder for most people.They will re-grow and spread. with a little time. Keep air exposure to a minimun between tanks and you should do fine.
If moving to the larger tank involves adding other rocks to the larger tank be sure it is totally cycled first before transfering the others cridders to the tank........