My experience of what I've seen, maybe I'm wrong about something:

the soldier is always winning first and then the archers.
if the archers are improved these hit other archers first.

the enemy always attacks the same soldier first

if there are several enemy units of archers hit the same unit.

if there are several enemy units of soldiers each soldier will hit a different unit of yours.

I dunno, i had 6 peeps, 3 archers(with steel shield and legion helm) and an axe man(steel shield and Legion helm) and 2 hammer men(again steel shields and legion helms) and they got their butts kicked to 2 sword man an axe man and 3 archers.  i believed we had the health advantage, but no go i lost all and they still had 2 sword men and an archer.  And this is after i Ran over the Entire BLOODY map trying to catch em, it would seem AI has higher speeds than us, man for man.

basically stopped playing today because of it

and yes my peeps were full health and there were no other interference.  

Knights are supposed to attack first in a battle.

Knights are attack before other troops, and archers are attacked last. Archers will shoot an random minion(even if that minion is already being fought), and all the other units will engage in a 1v1 with available enemies