Well, I figure that I'd better come to a conclusion here.
Situation #1 winner: For this one I figure I'd go with the one with a higher hand-to-hand skill level. Which is the Orc. Though it would still be an awesome fight.
Situation #2 winner: This one is a helluva lot harder to determine. Well, lets see. Orcs are supposedly the finest heavy armor troops in all Cyrodill. I feel like such a nerd right now. That is a plus for the Orcs. However, since the battle is taking place in the mountains(snowy mountains if I didn't make that clear), that could be a problem for the Orcs. Even though they are just as suited to snow and mountain terrain as the Nords. Though, since the Orcs ARE suited to that terrain, they would probably be more effective than other heavy armored warriors. As far as weapons, the Orcs will be devastating. With their many powerful weapons. Warhammers and Battleaxes and Waraxes and so on. The Orcs, I assume, would be as good as any on horseback and with archers. Nothing special. Same goes for the Nords. Though, in my opinion, the Nords would be a little bit better as archers. As far as armored warriors, the Nords are more wild barbarians than warriors. But they still have professional warriors. Just not as much as the Orcs. The Nords are known to use primarily light armor. Usually Fur or Chainmail. Or leather. The Nords are like Vikings. Using axes, swords, etc. The Nords, aside from their size, are your usual barbarians. I would think that the Orcs would be a bit better as battle tacticians than the Nords as well. My final verdict is that I think the Orcish army would be the victor of this battle.
Situation #3 winner: One on one would be different than army vs army. Lets analyze the combatants, shall we.
Orc: +10 Endurance, +5 Strength, -5 Speed, -5 Agility, +10 Block, +10 Blunt, +10 Heavy Armor, Also they have the Berserk power.
Nord: +10 Strength, +10 Endurance, +10 Blade, +5 Block. By the way, I'm only listing the attribute/skills that apply to this fight.
Orcish armor: "Based on High Elven designs, Orcish armor is an ornate but remarkably light steel plate worn over cloth padding. Light and comfortable in contrast to other steel plate designs," "This is the highest class of heavy armor that shops will normally sell."-Obliviowiki, Orcish Armor.
Nord's Fur Armor: "Fur armor is made from the fur of animals. It provides the weakest protection against enemy attacks, but it's the least heavy of all the armors."-Obliviowiki, Fur Armor
As far as weapons, the Nord's Battleaxe does more damage, the Orc's warhammer has slightly more reach, and the Nord's axe is slightly faster I think.
All in all. I think that the Orc is slightly more likely to win this fight than the Nord. Like, on a 60/40 to 55/45. As you can see it is actually quite close.
That's all for now. Catcha later!