I might go with He-Man as a Oath of Greyskull paladin, who has a channel divinity that gives him extra strength (or, in the spirit of the 1980's cartoon where he never hit anyone but could hit things, gives him the siege monster ability to do double damage to constructs). His other channel divinity could let him teleport magical armor from the armory of Greyskull to him once a day (for all the gimmick He-Man figures). I am not sure what oath spells to include, but oath of glory's spells might be a good starting point.
You know an Oath of the Watcher paladin looks like it has potential. I've been keeping an eye out for possible spell effects in the 2002 version. It's easy overlook possible spells due to the manga fighting style. So far it's arguable that he has used:
Absorb Elements (1st level ranger/wizard)
Jump (1st level ranger/wizard)
Compelled Dual (1st level paladin)
Thunderous Smite (1st level paladin)
Gust of Wind (2nd level wizard)
Counterspell (3rd level wizard/watcher paladin)
Find Greater Steed (4th level paladin)
You could argue that the interception fighting style could be merged with the monk deflect missiles to come up with his propensity to deflect Skeletor's bolts.
So far I am not getting a strong sense of any particular class but if Adam is a Level 3 beastmaster ranger (for Cringer (a panther), a level 2 paladin, with a view to advancing as an Oath of the Watcher paladin, I think that covers most of his bases.
The sword can cover off casting Tenser's Transformation and Summon Greater Steed, and then the magical armour that arrives can cover off the other classic abilities (Breastplate +1, +6 strength and constitution for He-Man, Barding +1 with enhance ability - Bear's Endurance for Battlecat).
Still observing the others but could do:
Teela - torn between level 8 battlemaster fighter with mobility and a level 8 swashbuckler rogue who can sneak attack with a staff.
Ram Man - level 7 champion with unarmed fighting style - adamantine plate mail +1 with resistance to bludgeoning damage and bonus damage on a charge
Mekanek - Level 7 scout rogue with darkvision, expertise in perception and a returning hammer
Stratos - Level 8 monster hunter ranger with wings of flying - not quite got to grips with his fighting style - seems to use pistols and rockets.
Man-E-Faces - Level 7 College of Eloquence bard with second skin dark gift from Ravenloft crack shot with a pistol but beyond alter self and some detection spells for his robot self I'm not spying much magic.
Buzz Off - Level 8 swarmkeeper ranger
Man at Arms Level 3 battlemaster fighter, level 10 battlesmith artificer
Orko Level 3 college of creation bard, level 7 wild magic sorcerer - Orko is very tricky - he mostly seems to levitate things so far and is definitely not trained in constitution saves.