Recently I just finished the imperial questline. every character i played iv'e done the stormclaok questline. and what I have noticed about the imperials is they only use swords,shields, and sometimes bows. during the questline I realized that the stormcloaks used multiple weapons. So does weapon type make a strategic difference in the war?(without the dragon born)

I feel like the Imperial Army has got a lot of organized parts to it including training and weaponry. With that in mind, I feel like the Empire has mostly trained soldiers in a singular way, sword & board or bow for ranged. They're probably exceptions, but it fits the lore of the Imperial Empire more to me. The Stormcloaks are more of a rough army, with the soldiers probably using their personally preferred weapons. The Stormcloak Rebellion needs as many soldiers as it can get, and probably doesn't have the same training or initiation as the structured Imperial Army.

I feel it is more "Nord" to run out into a fight swinging a giant hammer than an organized tactic like the Roman or Greek armies would use.

Stormcloak patrols usually massacare Imperial patrols when they meet.

Both sides usually only have light armour, the Imperials are armed with a bow and a sword, no shield, the Stormclaoks with a mix of two-handed weapons and sword and shield, with some having a bow as well.

I get the feeling that not only is the Legion relying on local recruits it can't even equip them very well.

You don't see many with heavy armour and you only see a couple of mages at Helgen. Certainly don't see any orcs in heavy armour who used to be the finest front-line troops of the Empire.