story identification - Novel where man wakes up in a random time-period find his services (as a soldier) are required

So, I've only read one of the books but I remember that it's a series. It's about a warrior who wakes up in a random space/time where he is needed to change the tide of a war that is going on, and when his efforts are complete he is pulled away and wakes up somewhere completely different. Probably from the mid-late '80s or early '90s... My soft cover version had a man in animal skins on it I think, retro cover, about 6" wide by 8" tall by 3-4" thick.

I realize it's not much to go on, but I really hope someone knows what it is.

Answer

You are looking for Michael Moorcock's Eternal Champion series. This is a large series of books that don't follow a single character but a kind of meta-character for which the series is named.

As summarized by Wikipedia:

The Eternal Champion, a Hero who exists in all dimensions, times and worlds, is the one who is chosen by fate to fight for the Cosmic Balance; however, he often does not know of his role, or, even worse, he struggles against it, never to succeed. Since his role is to intervene when either Law or Chaos have gained an excess of power, he is always doomed to be surrounded by strife and destruction, although he may go through long periods of relative quiet.

The name of the first title is Eternal Champion. Here's part of the plot summary (again, from Wikipedia) of this title:

The Eternal Champion is narrated by John Daker, an inhabitant of 20th century Earth. At the beginning of the novel, his sleep is disturbed by dreams of other worlds and a repeated name: Erekosë. After many nights he understands that he is Erekosë and he finds the strength to answer the call. He arrives in a world that is strange to John Daker but somehow familiar to Erekosë (the narrator struggles to reconcile these two viewpoints throughout the book). He is welcomed by the ageing King Rigenos of Necranal and his daughter Iolinda, and receives Erekosë's legendary sword Kanajana. The sword emits a deadly radiance that quickly kills anyone who receives even a minor wound from it. (Readers familiar with Elric will immediately recognise Kanajana as an Avatar of Stormbringer by virtue of its dark color and magical lethality.)

Rigenos explains to Erekosë that all of humanity is united in a desperate fight against the inhuman Eldren, who have claimed the southern continent Mernadin and are said to be seeking to expand their empire. (The Eldren have some resemblance to elves as depicted in the works of Tolkien and others, but the term is not used).