Can a carrier of salmonella typhi infect someone else via oral, vaginal, or anal sex?

Yes. Maybe. Yes.: One catches typhoid (typhoid fever) by eating or drinking contaminated food or beverages. Thus, one catches typhoid from a carrier if the food or beverages have been contaminated by the carrier. Oral sex and anal sex sort of mimic "the ingestion of contaminated food or drink" while purely vaginal sex is a bit safer, although that region of the body of a carrier is likely always contaminated.