Heterosexual - Attracted to individuals of the opposite sex.
Homosexual - Attracted to individuals of the same sex.
Bisexual - Attracted to individuals of either sex.
Transexual - An individual born as one gender, but who believes that their identity is that of the opposite sex. 1/2 of transexuals retain their sexual orientation after surgery while 1/2 reverses their sexual orientation after surgery.
Asexual - An individual who is not physically attracted in other people.
Pansexual - An individual who is not interested in others for their physical attraction, but rather, for their identity.
Omnisexual - An individual who is not interested in physical attraction and only interested in sexual gratification.
Homosexual: Gay and Lesbian individuals.
Bisexual: Bi individuals.
Transexual: Men who believe they are mentally women and women who believe they are mentally men. NOT necessarily transvestites, crossdressers, drag queens, or drag kings. Also referred to as Transgendered.
Asexual: People who are content to not engage in sex. Please note that individuals who have homosexual thoughts but are afraid to "be caught faking straight" may use this to diffuse suspicion.
Pansexual: Soul mates. For instance, individuals who fall in love with an individual who later becomes transgendered, but still retains the relationship. This is the ultimate in a long term relatioship free of sexual limitations, and ultimately choosing to be with an individual who mentally "completes" you.
Omnisexual: An individual interested only in orgasm. Straight men having anal sex or oral sex with other men (AKA on the down low) simply for the pleasure of it is an example. Please note that this has NOTHING AT ALL to do with physical attraction.
Attributed to Robert H. Heinlein, the priest of redheads, Explaining sexual orientation