어서 means quickly 오세요 means come (on) 들어오세요 come (on) in

오셔요 is short for 오시어요 = 오시(다) + -어요, where 어요 is a indicative or imperative sentence ending. The thing to note is 시 after 오, which turns a verb into an honorific(raised) form showing respect. So with the 오다 verb, you can say 와(plain form for friends) or 와요(오다 + -아요->오아요->와요, polite form for other adults). With 오시다, you have 오셔 (plain) and 오시어요(polite) which becomes 오세요/오셔요. 시 adds respect for the subject (who you're talking about) of the verb, which is different from 요 at the end which just makes the saying polite to the person you're speaking with. There can be four cases involving 오다 and 오시다. *와 = non-honorific, non-polite. *와요 = non-honorific, polite. *오셔.= honorific, non-polite. *오세요 = honorific, polite.