The Judds, daughter Wynonna and Naomi, were nominated for awards as entertainer of the year, the top award, plus vocal group, single, album and video.
The Judds have won CMA awards for top newcomers, vocal group and single record.
McEntire was nominated for entertainer, female vocalist, single, album and video. She was named top female vocalist in 1985.
Strait, a former Texas rancher who specializes in traditional country music, was nominated for entertainer, male vocalist, single and album.
Travis, a North Carolinian who has already seen his first two single releases reach No. 1 on the country charts, was nominated for male vocalist, Horizon (new star), single and album.
Also winning nominations for entertainer of the year were Willie Nelson and Ricky Skaggs, who won the award in 1985.
Finalists for the 20th annual Country Music Association awards are:
Entertainer of the year: Reba McEntire, Willie Nelson, Ricky Skaggs, George Strait and the Judds.
Top male vocalist: George Jones, Gary Morris, Strait, Randy Travis and Hank Williams Jr.
Top female vocalist: Rosanne Cash, Janie Frickie, Emmylou Harris, McEntire and Anne Murray.
Single of the year: "Bop" by Dan Seals; "On the Other Hand" by Travis; ''Nobody in His Right Mind Would've Left Her" by Strait; "Grandpa (Tell Me 'Bout the Good Old Days)" by the Judds; and "Whoever's in New England" by McEntire.
Album of the year: "No. 7" by Strait; "Lost in the Fifties Tonight" by Ronnie Milsap; "Rockin' With the Rhythm" by the Judds; "Whoever's in New England" by McEntire; and "Storms of Life" by Travis.
Vocal group of the year - Exile, the Forester Sisters, the Nitty Gritty Dirt Band, the Oak Ridge Boys and the Judds.
Vocal duo of the year - Crystal Gayle and Morris; Dolly Parton and Kenny
Rogers; Marie Osmond and Seals; Nicolette Larson and Steve Wariner; and Waylon Jennings and Nelson.
Instrumental group of the year - the Grand Ole Opry staff band, the "Hee Haw" band, the "Nashville Now" band, the Oak Ridge Boys band and the Strangers.
Instrumentalist of the year (four finalists) - Jerry Douglas, Johnny Gimble, Doyle Gresham, Mark O'Connor.
Song of the year (award to songwriter) - "1982," by James Blackmon and Carl Vipperman; "Bop" by Jennifer Kimball and Paul Davis; "Grandpa (Tell Me 'Bout the Good Old Days)" by Jamie O'Hara; "Lost in the Fifties" by Mike Reid, Troy Seals and Fred Parris; and "On the Other Hand" by Paul Overstreet and Don Schlitz.
Horizon award - Forester Sisters, Kathy Mattea, Seals, Travis and Dwight Yoakam.
Top video - "100 Chance of Rain" by Morris; "Grandpa (Tell Me 'Bout the Good Old Days)" by the Judds; "Honky Tonk Man" by Yoakam; "Who's Gonna Fill Their Shoes" by Jones; and "Whoever's in New England," by McEntire.