This is only going back as far as I remember with any decent recollection(97ish or so) and from watching big time games from seasons prior to that on youtube or highlight videos, so very likely I'm going to leave off key names from a lot of the older teams but it's not out of disrespect or thinking they're not worthy, just me lacking knowledge on the seasons they played.
I'll do the offense now and probably post the defense some time tomorrow.
QB: Peyton Manning
Reserve: Heath Shuler
Peyton is obvious, but I think some might pick Hendon over Shuler. I give Shuler the edge for Hendon playing in a much easier offense to put numbers up in(and much easier time to put numbers up in too), but I wouldn't blame anyone for putting Hendon #2. Guys like Clausen, Ainge, Kelly, Martin, Dobbs, Holloway and some others I'm sure I'm leaving off all were anywhere from good to borderline great, but they lack the Heisman-level play the 3 mentioned prior possess.
RB: Travis Henry
Reserve: Jamal Lewis
Henry's ability to dominate on the ground despite the years he played in being ones where our passing game wasn't quite to the level it was under Manning and Shuler in years prior is what stands out to me. Defenses knew he was getting the ball and it still didn't matter. Jamal Lewis earns the reserve spot here, but if you were to ask me, from all the backs I've watched take a snap in a Tennessee uniform, I think Jamal Lewis might have very well been the most talented one ever. He dominated his freshman season with Manning, and with having to carry a heavier load in 98 with Tee now at QB, Lewis somehow produced even more. A 6.8 yards per carry mark from a 5'11, 240 pound bruiser of a running back was absurd. His mix of size and speed prior to his knee injury is extremely similar to what Derrick Henry did at Bama and now on in the NFL. If he never got hurt, Lewis probably owns every meaningful Tennessee rushing record in the book.
WR: Joey Kent
WR: Peerless Price
WR: Marcus Nash
Reserve: Robert Meachem
Reserve: Carl Pickens
What a log jam at receiver, and could field a really good all-time roster using only 90s selections as a guy like Cedrick Wilson could take Meachem's spot. Kent, Price and Nash were an outstanding mix of athleticism and game IQ, undoubtedly assisted by working in an offense with Peyton Manning, a man known for demanding perfection out of his receivers route running. Robert Meachem went off in 2006, but likely could have had a great 2005 as well if not stunted by the god awful performance of the offense as a whole, but particularly Ainge and Rick Clausen's failures at the QB position. It was all made up for in 2006 though, showing off from the start of the season against Cal that he would be a force to be reckoned with. Some might pick Hyatt for this list given his record setting season, but I went Pickens over him(and guys like Stallworth and Washington) as not only was Pickens a fantastic athlete like Hyatt is, but his shiftiness in the open field is hard for Hyatt to match, and quite simply Hyatt does not possess Pickens' ball skills. Hyatt is also hurt some by getting to play in an offense that had him running wide open half his catches. He had to play a part in getting open as well, but if you gave the receivers on this list Heupel's offense, I think they too would have set records.
TE: Jason Witten
Reserve: Luke Stocker
Jason Witten might hold the biggest lead among best at his position on the entire Tennessee all-time team. Bill Anderson is likely the 2nd greatest tight end in UT history, but I've just not watched much of him. I went Luke Stocker over options like Rivera just to give an elite blocking/potential full back use option, but you can argue guys like Ethan Wolfe, David Martin or Mychal Rivera and I wouldn't fight on it. Stocker's combination of high level blocking and reliable hands get him the role for me though.
LT: Chad Clifton
Reserve: Michael Munoz
Offensive line is a position that gets a lot harder to evaluate if you didn't get to watch the teams live. As you go further back in years, replays and the like showing the offensive line and plays they did(or didn't) make becomes fewer and fewer, so the O-line will consist only of players I watched live. Chad Clifton is a great start for this, being a multiple time All-SEC selection as well as even an All American in his senior season. Being a starter(albeit his freshman year was at right tackle) for both the Manning era Vols and the Martin era Vols lets you know his excellence showed up in both pass pro and run blocking. Michael Munoz might be one of the more unfortunate stories of extremely talented players in our history. An absurdly talented tackle who managed to achieve a consensus first team all american selection in 2004, Munoz's career was riddled with knee injuries. While saying he would have gone on to be as good as his dad(NFL Hall of Famer Anthony Munoz) had it not been for the injuries would be a tall order to fill, he wasn't lacking in the skill and technique to give it a real try. Injuries are the only reason Clifton sits above him here(Clifton I believe started every game of his career, but I know never missed any major time), as Munoz when healthy was unquestionably the better player.
G: Cosey Coleman
G: Trey Smith
Reserve:: Dallas Thomas
Reserve: Jacques McClendon
I stuck with just the G designation here rather than specifying left or right given how frequently college offenses move the guards around, including the Vols over all these years. Cosey Coleman may have been 2nd to Clifton on those late 90s offensive lines, but it wasn't by much, being another outstanding blocker who like Clifton excelled in the high volume passing of the Manning offense and the ground and pound game after the switch to Tee Martin. Trey Smith is maybe a bit of an iffy selection with most of his starts here coming at tackle, but he was just as great at guard. Much like Munoz before him, he dealt with serious injury issues, but on the bright side they haven't prevented him from thus far having an outstanding pro career as well. Dallas Thomas and Jacques McClendon are probably good enough players to be starters on a lot of college teams all-star lineups, particularly if you're only counting since the turn of the century, Thomas in particular earning 3rd team all-american honors in his senior year.
C: Brandon Kennedy
Reserve: Scott Wells
Kennedy will probably receive the most "huh" reactions given the teams overall lack of success in his 2 seasons here, but Kennedy is the best center I've seen play for the Vols since my ability to actually understand the game developed. While good all around, he was an absurd pass protector. Despite blocking for some less than stellar QBs in 2020, I remember a stat read at the end of the season(Cole Cubelic speaking about who were some of the best o-lineman from the SEC that year on the radio), and he brought up that despite all the offensive struggles and playing like over 500 snaps, Kennedy had only allowed a single sack all season. Transferring to the train wreck that was the Jeremy Pruitt regime likely hindered what could have become an even better career for him. Wells was a really solid player, but he honestly makes this list more so as a "best of the rest" rather than a true standout. I could be blanking on a name, but Kennedy is the only center I can recall watching over the last 25 years that left any kind of impact on me as a viewer.
RT: Darnell Wright
Reserve: JaWuan James
Wright's accomplishments at right tackle over the last few seasons are numerous, but no indicator of his success is better than the fact that he was selected 10th overall in the draft to play right tackle, a move you do not see very often. The top 10(and for a lot of people the first round altogether) is generally preserved for left tackles/blind side protectors, but the Bears thought enough of his outstanding play to pull the trigger on him. James' accomplishments aren't too dissimilar, being selected by Miami at 19th overall in 2014. Apart of probably the most famous o-line in recent Tennessee history alongside the likes of Zach Fulton, Dallas Thomas and Antonio Richardson, James was viewed as the best of the group and his play certainly backed that up.