Not really. "Feeling wronged" sounds more like someone betrayed you by hurting you. "Taking offence" sounds more like someone said or did something you didn't like on an ideological level. If someone swore in front of you, or watched porn in front of you, you can be "offended", but you aren't "wronged", because it hasn't damaged anyone.
Sometimes they can be the same thing, though. Like if someone was racist or sexist towards you. Then, not only would you be hurt personally, but ideologically, their actions would be offensive as well.
Does that make sense?