殿方 (とのがた, 'gentlemen') is an old-fashioned, refined word for men. 共同生活 ('cohabitation, shared living') is the formal compound. ノーパン ('no-pan,' without underwear) is slang. 慎みなさい ('show restraint') uses 慎む ('to be modest/restrained') in the ~なさい imperative. The collision of elegant vocabulary (殿方) with crude slang (ノーパン) is the comedic core.