of Theoden's battles?

[The Saucepan Man]

Throughout the history of Rohan, following the grant of the lands by the Steward Cirion to Eorl, there had been frequent incursions by the Dunlendings who believed that much of the land was by rights theirs. At times, as I recall, the Men of Umbar were also involved in attacks on Rohan.

These were not "very small skirmishes with surrounding Goth/Vandal types" but full scale battles and seiges and, on occasion, Rohan came pretty close to defeat. At times, they verged on civil war as a result of intermarrying with Dunlendings in the west. No doubt the Dunlendings' incursions continued up to and during Theoden's reign (by which time they were almost certainly being encouraged by Saruman).

Yes, and Rohan was subject to raids by Orcs from the Misty Mountains too. Eomer's father was killed in one such raid.

Read the Appendix A to LotR for further information.