In NG+1, I have two characters whose levels have maxed at 100 and no longer get any XP. However, I've found some loot that has even higher level requirements, like level 101 and level 105. So I was wondering...

If I go to NG+2, will I then be able to gain more levels (at least for more Ability points, if not Skill points)?

I believe you could only wear those by reaching the stats requirement.

So you either have to distribute your stat points to match those of the item or meet them by equipment bonus (or set bonus) / stat enchantments / socketables. (Or combination of any/all of these)