Strayer was born in Moose Jaw, Saskatchewan. In 1959, Strayer graduated from the faculty of law at the University of Saskatchewan. He worked at the Department of Justice in Saskatchewan until 1963 at which point he began teaching at the University of Saskatchewan. He eventually became the Director of the Constitutional Law Division of the Privy Council Office. In 1974, he was appointed Assistant Deputy Minister of Justice where he spent several years working on first drafts of the Charter.