If you give your OBS settings, I could try to see if there is a problem with them and not your CPU..
But if you do want a new CPU, an I7 4790 or 4790k (if you want to overclock) should be your cheapest option to stream at 720p 60fps, which is the max quality I would recommend streaming at. The 4770 would probably work too, but the 4790 is about the same price (on the site I checked) and is slightly better so that's what I'd recommend. It goes for $300 in the US, so about 270€.
Posting a Logfile would have been easier.
But right now you are trying to stream with NVENC anyway so your cpu pretty much has no impact here.
If not going with an i7 4790 / 4790k or an xeon E3-1231v3 / E3-1241v3 should be the best, the Xeons are by far cheaper than the i7
Umm how do i post the logfile? i tried upload a file but it doesnt let me :oI will stream today and send the logfile :)