With DCs of 15 you're proposing a CR1 skill challenge. Should be close to a gimme for any of the parties listed.
So how does the Fighter with the 8 Int, who has Level + 3 skill points, total (2 per level -1 for Int modifier = 1 per level) contribute? Particularly when the Social skill challenge involves skills that are all cross-class?
While details of the challenge matter, at a minimum he can attempt to Aid Another at something. The skills you described are Wisdom and Charisma based. Unless he made all three dump stats (Int, Cha and Wis), he'll be at a -0 in at least one of those areas. He has a 55% chance of succeeding on his Aid Another check. And that's true at any level.
One thing to be aware of is which checks are critical, where failure in one roll means failure in the entire enterprise.
For example, in your social scenario, if the famous (or infamous) Barbarian introduces himself to the Lady of the house, loudly and by name, and begins to brag of the monsters he's killed, and the women he's taken in his career.
In essence, a player someplace decided to have their unskilled character "contribute", and rolled a 1. Or maybe the player himself has decided to blow this one off and get back to killing things, who knows.
In that moment, the party failed. There is no recovery from that one.
In a stealth scenario, say the party is trying to sneak past the perimeter guards of an enemy encampment. One failed stealth check and the whole thing is blow, the jig is up.
Say the party has a Paladin, all glowy/shiny in his armor, whose plate mail gives him a total negative on his stealth check. He's not going to be able to roll even a 10 to Aid Another, and there probably aren't enough Aid Another dice in the world to let him make it. How does he get by, or even help?
By being creative: He can't enter that camp unseen and he knows it. He clanks when he stands still. So he decides to enter the camp, seen. He presents himself at the front gate, asking for an audience with the commander. Attention will be given to that area, drawing guards away from other spots, and distracting others.
He (or she, let's not be sexist) has thought of a way to use Bluff, a Charisma based skill that he/she is better equipped for, instead of the Stealth check. The player's found a viable way to substitute one skill for another, and thus gain a possible Success in the challenge.
So it's important for a DM, in any system or scenario, to keep an open mind. Players should always be allowed to propose alternate solutions in any Skill challenge.
Over all, a Dm has to "Wear two hats". When planning an encounter, he plays the part of the enemy, laying traps, planning defenses, distributing forces or planning the use of spells. The DM is, at that moment, the adversary of the party, and should be working towards their defeat and/or destruction.
However, once play starts the DM has to "change hats". No longer the adversary, the job now changes to impartial arbitrator of the rules. It's now okay to root for the PCs, as long as you handle things with an open mind and an even hand.
And that last part says, if the players propose an alternative solution, one you as DM didn't see or consider, it's okay to say "Yes".