When Hadeth rebelled, and was cast out of heaven, many of the powerful spirits joined her in her rebellion. These spirits had many different reasons -- Asmodeus thought that he could bring a stronger order out of the chaos she would create, one that had him as it's master. Dispater out of loyalty to the dark general. And Mephistopheles out of resentment of the new order that Fayon had created after his ascension. During the war, especially as it grew more desperate, Hadeth grew more crazed, seeking allies wherever she could find them -- most infamously, Miska the Wolf Spider. The devils grew more and more concerned, but they would do nothing. They had, after all, sworn her oaths. They served her loyally during the war, but once she was imprisoned in Hades, they did not believe serving her would bring any more gains. So under Asmodeus's leadership, they crafted realms in the underworld they called hells, and seek to increase their power by corrupting creation.
When they are not engaged in creating enormously complex plots of betrayal and counter-betrayal, the devils are trying to corrupt souls. The economy of hell runs on souls, but the only way devils can get souls is to convince a mortal to freely agree to give theirs up to them (typically, a soul is claimed by Hades upon death). Fortunately for the devils, men are greedy and short-sighted, and are often willing to make a deal. Asmodeus has proven adept at maintaining power despite many upheavals.