Nurse, 31, will be entering his 13th season after spending all 12 of his NHL career with the Oilers. The Hamilton native put up 24 points (7 goals, 17 assists) in 82 games this past season - the lowest since his second full season in the league (11 in 2016-2017).
His 88 giveaways last season were a career high.
Mukhamadullin, 24, is entering his fourth season. The Russian put up just 12 points in 50 games last year for the Sharks after averaging a career-low 17:09 average time on the ice.
Sharp, 20, had five goals and 14 assists for Western Michigan this past season before being taken in the fourth round of this year's NHL draft.