This question relies on premises that are not true of D&D 4e play.

For the purposes of this question, please assume that I have four characters in play.

If the "I" here refers to a single player, you will not typically have four characters, just one. If the "I" here refers to a DM and his or her four players, that's more reasonable, but the presumptive speaker then bears more burden for the resolution of the following.

They all have "Acrobatics" skill. They are 1st, 5th, 10th, and 15th levels respectively.

Those four characters would not be "in play" together — they range all over the heroic and paragon tiers, and things that would be a suitable challenge for one might be trivial for another and an insurmountable obstacle for the last. (This is particularly true if one of the characters has not just trained in Acrobatics, but is focused on it, as a rogue might be.)

They are in a bar and they want to swing on exactly the same chandelier to impress a fair maiden on the other side of the room.

So, which is it to be: Acrobatics, to swing on the chandelier, or Diplomacy, to impress the maiden? :) What's the end result of this maiden being impressed? If it's just to pass the time, perhaps this could be addressed quickly and without any rolls at all.

What is the difficulty class for the swing? Why?

In this hypothetical situation: the difficulty class for the swing should based on the tier of the campaign being run. As the DM, you'll know what that is, and set it accordingly. The other characters should treat the chandelier as an element of the scenery: either they have the skill to surmount it easily, or it's entirely out of their league.

What if all the characters were the same level? What is the difficulty class for the swing? Why?

This has been addressed in other answers: use this table and set a DC appropriate to the circumstances of the bar. (Slippery floor? Tables to run and jump on to gain height?)

This question relies on premises that are not true of D&D 4e play.

For the purposes of this question, please assume that I have four characters in play.

If the "I" here refers to a single player, you will not typically have four characters, just one. If the "I" here refers to a DM and his or her four players, that's more reasonable, but the presumptive speaker then bears more burden for the resolution of the following.

They all have "Acrobatics" skill. They are 1st, 5th, 10th, and 15th levels respectively.

Those four characters would not be "in play" together — they range all over the heroic and paragon tiers, and things that would be a suitable challenge for one might be trivial for another and an insurmountable obstacle for the last. This is particularly true if one of the characters has not just trained in Acrobatics, but is heavily focused on it ("all in"), as a rogue might be.

They are in a bar and they want to swing on exactly the same chandelier to impress a fair maiden on the other side of the room.

So, which is it to be: Acrobatics, to swing on the chandelier, or Diplomacy, to impress the maiden? :) What's the end result of this maiden being impressed? If it's just to pass the time, perhaps this could be addressed quickly and without any rolls at all.

What is the difficulty class for the swing? Why?

In this hypothetical situation: the difficulty class for the swing should based on the tier of the campaign being run. As the DM, you'll know what that is, and set it accordingly. The other characters should treat the chandelier as an element of the scenery: either they have the skill to surmount it easily, or it's entirely out of their league.

What if all the characters were the same level? What is the difficulty class for the swing? Why?

This has been addressed in other answers: use this table and set a DC appropriate to the circumstances of the bar. (Slippery floor? Tables to run and jump on to gain height?)