What do these episodes have in common?

Friendship

Beaver Runs Away

Larry Runs Away

June’s Birthday

Larry’s Club (when Larry had a made up club)

Is it that Mrs. Mondello is in all of them, and they all probably have a scene at the Mondello house?

Close enough. Beaver is at the Mondello house inside only. In Beaver’s Prize he’s outside the house and also Found Money in the yard. There could be others.