Tolkien didn’t write too much about the Woodmen, although they exist on the periphery of several of his stories.
The Woodmen were originally descendants of members of the House of Beor and the House of Hador (though at the time it was known as the House of Marach) who settled in Mirkwood during their westward migration in the First Age. As such, they are related to the Edain, but didn’t actually have anything to do with Beleriand or Numenor. It’s hard to tell if the Woodmen were related to the Northmen of Rhovanion, or if they were actually all the same people who just happened to live in slightly different places (as in, the Wodmen were actually Northmen, but since they lived in Mirkwood instead of just to the east of it, they were called Woodmen.)
All that we really know about the Woodmen society is that they lived in western and central Mirkwood. As they lived primarily in the forest, they couldn’t have relied too much on farming (it’s possible that they traded with nearby agricultural communities to make up the difference in food supply.) Honestly, there isn’t much that’s “special” about the Woodmen in general.
Because of their location, though, the Woodmen sort of get dragged along by Mirkwood’s story in the Third Age. As Sauron’s presence in Dol Guldur grows, the lives of the Woodmen becomes more difficult (having to deal with orcs and spiders on a fairly regular basis.) Their people experienced a bit of a revival during the years after Sauron left Dol Guldur, though when the nazgul arrived in Dol Guldur only a few decades later, it’s likely much of this progress was halted.
After the War of the Ring, it seems like the Woodmen’s future is looking up: after the elves of Lorien and Mirkwood destroyed Dol Guldur and removed its evil presence from Mirkwood for good, the entire central portion of Mirkwood was given to the Woodmen and Beornings (the descendants of our friendly neighborhood skin changer, Beorn) to share. I can’t say anything about their earlier history, but to be given so much land (which was bordered directly on the north and south by the elvish realms of Thranduil and Celeborn), the Woodmen were either already on good terms with the elves, or they were about to be.
SOURCES: LOTR, LOTR Appendices, The Hobbit, The Histories of Middle Earth vol. 12 (“Of Dwarves and Men”)