I went to university there for 4 years.
Sorry Volk, I have to disagree with you, but mot of the the university students leave town during the summer. (This doesn't mean that there are no targets in the city, but there is more to choose from during the semesters.)
Basically, in summer, the best place to hang out is Szechenyi Square, lot of open bars, many people drink there. One of the most popular places there is Aftersix.
During weekdays you should check out the university parties in Bahnhof (Lapos) or Bridge Club. They are located right next to Szechenyi University.
http://bahnhofgyor.hu/lapos/lapos/
http://www.bridge.szeportal.hu/
During the weekend it's best to check out Mamma Mia club, right on the bank of the river.
http://www.clubmammamia.hu/
If you are more into techno music, there is a huge two story place on the outer ring of the city, it's called Vertigo.
http://www.clubvertigo.hu/
They recently opened a new club called Mundo, it's supposed to be hot right now, but I haven't been yet. I can't find a website to that, but theey have a page on Facebook.
Regarding language, most university students will speak english on varying levels, as it is required to take classes in foreign languages, and english is way more popular than german and other languages. German was the number one foreign language studied in Hungary, but not anymore.
Let me know if you need any more info.