Would a family history of colon cancer make me more likely to get anal and oral cancer also?

NO: Anal and oral cancer share one risk factor in common: the human papilloma virus (hpv). A family history of colon cancer does increase the risk of colon cancer. Remember to get your colonoscopy.

Rectal yes: Family history of colon cancer especially in first degree relatives does increase your risk for colo-rectal-anal cancer. I don't believe there is an increased risk for oral cancer.

No: Anal cancer is distinct from colo-rectal cancer as it arises from different cell type - squamous cell. There is no diffinitive increased risk of anal or oral cancer in those with a family history of colo-rectal cancer.

No: No studies I know of suggest this correlation.