As Stabbey said, the social skills are not strictly necessary. Charisma helps with the rock-paper-scissors minigame, but so does save+load
There is only one quest (in the original game) that I know of that needed charisma 5 to get the most out of, but all in all charisma can be down-prioritized. Not sure how important it is in EE.
Barter is nice, but not necessary. It helps with your economy during the early game, but later on you will be swimming in money (at least if the EE version is similar to the original one).
Lucky Charm is nice just as Barter. It helps you get better loot and can be a good boost to your economy early game, but later on it is not that useful. I do not think you will get a higher chance to get legendary items, but I do not know if this is the case or not.
Telekinesis is very useful since you can grab loot from longer distances, but is strictly not necessary. What you can achieve with it can normally also be achieved using your teleport pyramids. Although it might be necessary for you as a player in order to not get too annoyed during playing this game. Getting close up to every loot item in order to grab them can get a bit tiresome in the long run.
Your lead character should have high Perception in order to avoid traps, find secrets etc. I recommend that your lead character is also main talker. That will save you a lot of hassle since you do not need to change who is doing what all the time. This is just for convenience, it is not necessary.
Pet-Pal is important, but need not be on your main talker. A wizard with pet-pal and Lore makes perfect sense. You just need to select the wizard whenever you want to talk to animals instead of your main talker (assuming they are two different characters). I just find it a bit easier if I can have the same character do most of the things in the game.
Notice that there are a lot of items that gives boots to Charisma, Crafting, Blacksmith, Lore, Telekinesis and Leadership, so you normally do not need to raise them to a higher level than 3. Sometimes you can even get +3 from items. Item bonuses stack, but you will only find them on certain item types, so you will normally not get more than a +2 bonus to a skill.