This is my attempt at a viable solo Rohan themed Elfhelm deck. Obviously you want to get mounts on the heroes as soon as possible, but there are some other key cards to make this deck tick.
Gamling is super important, because discarding allies to power various card effects is the age old Rohan strategy. Here it works particularly well if you can cycle through an Escort from Edoras each turn, returning it to your hand, boosting Éomer's potential attack to eight (with Firefoot), while readying Éothain if you have him out on the table.
Questing was surprisingly decent, utilising the combo above, but also by getting Windfola and Snowmane on Théoden (for questing of four), combined with Grimbold and the West Road Travellers. While there isn't a lot of card draw, there is some with Valiant Sacrifice, but there are also a number of fetch cards (Mustering the Rohirrim and Westfold Horse-breeder).
The songs help smooth your resources, but also boost your stats due to Elfhelm's ability. After questing for four, then readying with Snowmane, you could potentially have Théoden attacking for four (or eight with Herugrim!). Combined with Éomer, that's plenty of attack power.
Certainly not a power deck, but good enough against a variety of quests, and a lot of fun. Most enemies won't last longer than a single engagement with you!