I'm setting up a tabletop RPG campaign set in a viking-esque fantasy society, and I'm trying to get a basic idea of the social structure, taking my limited knowledge and filling in the gaps with whatever sounds good, but I'm getting stuck on the title topic. I don't know anything about it and I'm not sure how to even formulate a google or scholarly search to get what I'm looking for. More specifically:
The following short answers are crude summaries of the previous posts below, mainly answered by /u/sagathain, /u/textandtrowel and mine.
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1: Were viking expeditions (to raid, trade, or whatever else) organized by lords or independently by freemen, or both?
I suppose (as I argued before in the second linked thread) that the ownership of the ship was the key to understand the situation better. Both organizing principle can be confirmed in contemporary source like runic inscriptions, but the former was probably more common especially for raids.
2-a: If by lords, was participation voluntary or compulsory?
I don't think individual military followers (lið, hirð) of the ruler had much to say for each expedition, but to join in such a military retinue of the lord itself seemed to mainly be voluntary. The skald (poet) list from medieval Iceland suggests that a single poet who served several rulers throughout their life was not so rare.
As for the larger fleet like the notorious Great Army of the expedition of king of the Danes in the beginning of the 11th century, several smaller band led by individual chieftain often joined in the joint-expedition. In other words, the Viking 'king' inherently had difficulty in maintain such a large size of the fleet unless the expedition (and successive payment) went well, and it sometimes led to the estrangement of the part of the fleet. In such a case, the participation to the large expedition fleet was also primarily voluntary.....though I cannot refute the possibility that some subordinate magnates were de facto forced to join in.
2-b: If independent, how much say did the relevant liege(s) have, could he just veto the whole thing?
As for joint-ownership, it is reasonable to suppose that each joint-owner of the Viking ship (either for war or for trade) partly have something to say for the expedition.
3: Who went on expeditions? Was it just vassals of the organizing lord, or broader than that? Were thralls ever pressed into expeditions? To fight or just as labor?
As I summarized in the answer to OP's first question (1), mainly military retinue, but sometimes independent freemen might plan the expedition jointly. As for the thralls' possible presence in the expedition group, high-medieval Nordic naval conscription system called leiðangr, found in medieval law books from the 13th centuries and primarily intended for the defense, allows the farmer to substitute their own obligation of participation with the thralls as cooks (Cf. Older Gulathing Law, Chap. 300). I also suppose that such thralls had little choice to join or not at least officially, but at least they seemed not to be expected to fight together with other crews who primarily joined in the expedition spontaneously.
You can also find some introductory books on the Vikings in the third linked thread above.