Adenians pwn imperials.
An army of Adenian heavy cavalry, with help from Paladins of the One, mercenary cavalry, and a few Swadian and Vaegir knights and Khergit lancers have no trouble with large imperial armies in the field, especially in open country. The imperial cavalry are tough, but there are never very many of them.
In sieges - first, make sure your castles and towns have lots of troops. 1000 or more is helpful. It would be handy to know where the invasion is coming from, but we don't get to know, in spite of messages that "the imperial army is seen just over the hills." Apparently we can see the army but not which hills they are behind. Even a little warning allows some troop transfer and concentration of lords. The imperial army will bypass centers with large armies, looking for easier game. I had 7000 troops in Yalen and the entire imperial army just went around, heading for Nord country.
Siege armament includes a masterwork heavy crossbow, 2 large bags of steel bolts and a balance northmans axe. Station for a clear shot on the ladder or tower and headshot. But I may switch to a glaive or halberd, trading reach for speed. After the attack is broken, trade the best cavalry into the army and attack the imperial army remnants.
After the battle, recruit as many troops as possible. Place infantry and archers in centers and keep cavalry.