As you can imagine, this is a very controversial topic, so many opinions you will hear about it on the internet are heavily influenced by nationalism from both sides. I'll try to be as objective as possible.

Wikipedia says that historically there were more Romanian people living there than Hungarians

That depends on what you mean by "historically". It is definitely true from the 19th century and onward, but whether it was true before that, we can only guess due to the lack of census data. The first official estimation to the demographic breakdown in Transylvania is the estimation of the the Austrian administrative authority (Verwaltungsgericht) from 1712-1713. According to that the population of Transylvania was 47% Hungarian, 34% Romanian and 19% Saxon. However this is not based on census data.

For the reason why both nations claim this territory we need to go back much further. The Hungarians conquered Transylvania in the late 9th century and that's when they started settling it. After that, Transylivania was under Hungarian leadership until the Treaty of Trianon in 1920 (except for the rule of Mihai Viteazu, a Romanian who ruled it from 1599 to 1600). Then nobility were all Hungarians, while the burghers were mostly Transylvanian Saxons (we know this, because they were the more well-documented classes). As I've said before, nobody knows the exact ethnic makeup of the region before the 19th century censuses, so we don't know the nationality of the serfs who lived there. The Hungarians claim that the region was majority Hungarian before their 150 years war with the Ottoman Empire left the Central parts of Hungary depopulated, which resulted in the invitation of foreign settlers from neighboring countries and mass immigration to the now empty lands in an attempt to repopulate the country. This is where the Hungarian claim comes from.

However, nobody knows for certain who lived there before the Hungarians arrived or when the Romanians arrived there. The Romanians claim that they were already present before the Hungarian invasion, however there is no convincing evidence to support or disprove this claim, so there is still an ongoing debate about it. The other theory is that they arrived in the 12-13th century. So this is where the Romanian claim comes from.

Why not to the Germans settlers in that area? That land was given to us by the Hungarian King, so we would protect his border. Some ducuments say, that the Romanian still lived behind the Karpaten Mountains at that time and that they settled later in Transilvania.

as Muhu stated there is no official census data from before the 17th century about the ethnic separation. before 1920 Transylvania was mostly a part of KoH or the Ottoman Empire or the Habsburg Monarchy.

since KoH was a multicultural country, nationality was not that important before the 19th century. folks tolerated eachother and lived and died together in war and peace.

and nationality was not a factor either when the Antant made peace with Austria-Hungary after WW1 and redraw its borders. for the Antant the only important thing was to have a few loyal anti German and anti Austria-Hungary allies in the region, and they bought their loayality with a piece of land.

so you see this hate thing is realtive new. what really pisses hungarians is that the old and new neighbours received historical KoH lands with little effort, just by promising they will support the Antant.

dont know the Romanina pow though...