I was wondering where the Orcish people stand in the civil war within Skyrim? Doesn't Ulfric and others prefer Skyrim being a nordic country for nords, thus usually rejecting or looking down upon other races?
From other TES titles, I remember that the Orcish smiths and warriors were highly praised in the Imperial Legion. Would it make more sense to join the Legion instead of Stormcloaks?

Depends on your characters role-play...

I had an Orc that joined the Imperials because they have been known to be smiths and warriors for the empire in the past...

I also had an Orc that joined the Stormcloaks to show the Nords that Orcs are honorable warriors...in the same way that I had a Khajiit join the Stormcloaks to show the Nords that not all Khajiit are pickpockets and thieves...

Note that even though Orcs are prized in the Legion, apparently the Imperial populace is still bigotted against Orcs. Just talk to the Orc at the Solitude Sawmill to learn just how Orcs are treated by Imperial supporters.

I think Orcs as a whole like the Legion because it offers them opportunity to travel the lands. The Legion also welcomes the Orcs as they are masters in Heavy Armor and Smithing.

Many of the Orcs in the cities (like Markarth) served in the Legion.

Orcs in general, while not showing any particular love or hate for the Empire itself, does have traditions on joining the Imperial Legion, ever since they forced the Empire to accept them during the Warp in the West. The Legion has been their way of winning acceptance with the other races of Tamriel and, if you listen to some Orcs in Skyrim, a way to escape traditions they don't want to live by and see the world.

I don't think the Orcs have much of an opinion on the Civil War at all, at least not as a population. Their strongholds have been in Skyrim at least since the Merethic(if the Wise Women are to be believed when they say their presence outdate that of the Nords in the land) and, while there have been some conflicts, the Nords and Orcs have gotten along reasonably well on Tamrielic standards. Who rules Skyrim wouldn't matter much to them. If they'd join the Legion, it is because it is the Legion, not because it is the Empire.

Note: Nothing of this has to apply to individuals. This is a general tendency description based on the available information.

The legion just likes to use them because they make good weapons and armour.

And because they're ferocious on the battlefield.

While that is true to an extent, I'd recommend that you don't leave out what the Orcs have gained through serving in the Legion: Acceptance. It really was a turning point for the Pariah Folk when they were given the chance to join the Legions and show more of themselves and their skills to the rest of the races. In the last 230-something years, the Orcs have been more accepted than any other period in known history, ultimately giving their people an easier time.

Of course, they had to force the Empire to recognize Orsinium as a kingdom under their protection and even allowing them to serve the Legions to begin with, so the Empire was hardly anywhere near saintly about that. Overall, serving the Legions have been a good deal for the Orcish people though.

As Tdroid already mentioned, Orcs generally join the legion because that is where they are respected and prized the most even when compared to other races serving in the legion, not because they actually want to serve the Empire and it's interests. It's one of the few if only places where Orcs are actually treated with any respect at all, let alone more respect than most races.

I do not feel the Orcs feel one way or another. It is likely entirely personal.

They're neutral.