Transexuals- people who feel they are one sex even though biologically they are the other.
a. An example of this is in the episode "Quagmire's Dad". Quagmire's dad comes to visit his son and confesses that he will be getting a sex change operation. He says that he has always wanted to be a woman. Quagmire is shocked at first, but then comes to accept this change.

Homosexuality- sexual attraction to someone of the same sex
a. This can be seen in the episode "Family Gay" where Peter, while participating in medical studies, receives the gay gene. This episode then focuses on Peter and him becoming gay. He leaves Lois, moves in with another man, and starts a new life.

Heterosexism- a view that labels anyone who is not heterosexual as "queer"
a. This term can be seen also in the "Family Gay" episode. In this episode Brian and Stewie enroll Peter into a straight camp. Before they do this though Stewie makes a comment and Brian responds with the question, "Are you queer?" Brian is labeling Stewie as gay just for a comment. Joe also calls his friends queers because he becomes upset. The actions were considered gay and therefore they were called quer.

Abortion- the deliberate termination of a pregnancy.
a. In family guy there are a few episodes that poke fun at abortion. One particular episode states that abortions having been going on since the beginning of our nation. This episode show pregnant women walking off a ramp and falling on their stomachs as means of an abortion. Family Guy pokes fun at both sides the the abortion issue; pro-life vs. pro-choice.

Pornography- sexually explicit material intended to cause sexual arousal.
a. In an episode where Peter tells Quagmire about "that internet porn", Peter can't find Quagmire out and about for the next few days. Finally one day, Peter is outside and Quagmire opens up his door to go outside only to seem like he hasn't seen sunlight in weeks. He hadn't shaved in a long time and he tells Peter that he's been checking out "that internet porn" and he hasn't done anything else. He finally ends the conversation by walking back inside only to reveal that his left arm is absolutely jacked.

Prostitution- the selling of sexual services.
a. When Peter is struggling for a few days as he's between jobs, the kids ask Lois what he's going to do. As they're driving through town they see Peter dressed as a female on the side of the road acting as a prostitute to try to get money. Lois is outraged and when she tells him to get in the car he says, "ok but it's going to cost you!".

Sex- the biological distinction between females and males.
a. In that same episode where Peter tries to become a prostitute, he tries to create an image that makes people think he's a girl. However, biologically his sex is still the same as you can still see that he is clearly a male.

Heterosexuality- sexual attraction to someone of the other sex.
a. Probably the best example of heterosexuality in Family Guy is shown through the character Quagmire. He is shown in the show as basically being addicted to sexual activities with females and commonly talks about females in a provocative way. He even asks Peter if it's ok to have a relationship with Lois and even Meg.

This picture depicts Peter after he receives the "gay" gene from a procedure.

Quagmire's massive arm after being addicted to pornography