I'd use him to flesh out DC's Cosmic arena. Give more spotlight on their space heroes and villains.
In particular, I think Mongul would be a great villain for Thor, always wanting to make him his top gladiator and throwing various other powerful alien warriors at him.
Lobo would be a great rival, since he's got qualities Thor would admire, like his fortitude and his personal honor code, but at the same time would be disgusted by his general savagery and disrespectful attitude. I can see them being drinking buddies after a fashion.
Rounding things out, I'd hook him up with Maxima. Thor would certainly be more Maxima's speed, being a warrior and a prince, and while he'd certainly respect and likely be attracted to her power and warrior skill, he would find her arrogance off-putting, since he had the same problem himself. I could see him influencing her to be more honorable and compassionate, while at the same time not being unwilling to give her the dick.
Him butting heads with Orion and slugging it out with Kalibak would be good, old-school space mythology fun, and I'd love to hear him weigh in on Darkseid's tyranny, something along the lines of, "Dark one, you rule in blood and fire, but thy reign shall end in thunder!"