Gresham played at Big Creek High School in War, West Virginia, under WVU alumnus Joel Hicks. He was second team All-State and earned 10 letters in high school (4 in football and 3 each in basketball and track).

In his first season at WVU, he he scored 130 points and rushed for 1500 yards on a team that went 9-1 his senior year. As a sophomore, he rushed 71 times for 160 yards with a 2.3 average. He also caught seven passes for 99 yards and scored three touchdowns. In his junior year, he led the Mountaineers in rushing with 1,155 yards in 206 attempts, a new season record. He scored a total of 10 touchdowns, nine of which were rushing, and rushed for 109 yards on 16 carries in the Peach Bowl. He was the 11th leading rusher in the nation in 1969 and also caught 15 passes for 147 yards and returned 6 kickoffs for 188 yards. His best game was against Tulane when he rushed for 169 yards. He ran a 9.9 100-dash and also ran the 440-yard relay for the Mountaineer track team.

Gresham was named Associated Press All-America honorable mention in 1969. Overall for his career as a Mountaineer, he rushed for 2,181 yards with a 6.2 yards-per-carry average his senior year and ranked 11th nationally in rushing. He was drafted in the eighth round by the New Orleans Saints. Gresham was named Rookie of the Year by the Saints and Sinner Club. In his six years of the services with three NFL teams including the New Orleans Saints, Houston Oilers, and the New York Jets, he totaled 1,360 rushing yards for a 3.3 yards-per-carry average and 12 touchdowns. Also, he had 90 receptions for 728 yards for a 8.1 average and one touchdown. Gresham had 46 kickoff returns for 1116 yards with a 24.3 average per return. His best year was 1973 when he had the NFL's longest return of the year, a 103 yard kickoff return for a touchdown against Cincinnati, and was sixth in the AFC in kickoff returns. Gresham was the second leading rusher behind Fred Willis with 400 yards on 104 carries for a 3.8 average and two TDs.