From a person who's used enough of Omegle to know its basics.
One thing I have to say: Do NOT go on Omegle if you are easily insulted. It is not for the faint-hearted as well. Almost all of the Omegle community is in love with Hitler. I have seen too many Holocaust and 9/11 jokes. One thing I see too much as well is "Are you horny?" or "ASL?". The "N" word is one of the most commonly used word, as well as other derogatory terms for homosexuals, Jews, Muslims and others. About 1 out of 2 people is a pervert, and many, many questions on Spy Mode are disgustingly inappropriate.
That said, you can find a few people worth chatting with, and I have to say, it was truly worth the struggle of skipping those dumb questions. A tip I have: Put interests in the Interest box before chatting, so that you can talk to people who like the same things as you do. With this, I found absolutely no undesirable person for a long time!
So, as a 15-year-old who knows what she's talking about, take my word for it. Maybe people of that age might have a hard time with Omegle, so just wait until you feel comfortable with these things.
What other families should know
Too much violence
Too much sex
Too much swearing
Too much drinking/drugs/smoking