Theoretically, it should be a rounded-lip sound as well.Here's a recording of the sound in orgueil vs. the one in eux. The main difference, I think, is in the rounding or not of the lips. The lips are rounded in eux, not so in orgueil, or at least much less.
Yeah, right, the lips are rounded — just less than for eux, or maybe just differently... the lips protrude less.Theoretically, it should be a rounded-lip sound as well.
As I have written above, the sound in eux, /ø/ (German ö) should be an é, /e/ (as in passé or like the German e in Leere) with rounded lips.
The sound in orgueil, /œ/, should be an è, /ɛ/ (as in crème or like the German long ä in Ähre) with rounded lips... well, I'm not French (and neither are you ... but you seem to know the language quite well), but maybe you can try it: the difference between è and /œ/ should really just mainly be the position of your lips.