”Sexual orientation” is an enduring personal quality that inclines people to feel sexual attraction to certain kinds of people. Sometimes sexual orientation is also used to include romantic orientation, the tendency to feel romantic attraction to certain kinds of people. Words for orientations involving non-binary people are, at this time in history, not satisfactorily developed or agreed upon.
Orientations tend to be named and categorized in a way that involves one’s own gender identity. For example, “lesbian” indicates not only that one is attracted to women, but also that one identifies as a woman. Some words for sexual orientations make reference to one’s own gender: heterosexuality and homosexuality, gay and lesbian.
Some words for sexual orientations don’t make reference to one’s own gender, which makes it easier for nonbinary people to use them. This includes androphilic, gynephilic, skoliosexuality, and asexuality. This is also the case for bisexuality, polysexuality, omnisexuality, and pansexuality, which mean attraction to more than one gender of people. People disagree about how each of these involve transgender, nonbinary, and intersex people, and which of these words is the most inclusive and respectful of the legitimacy of them.
Here follows an alphabetical list of sexual orientations, with short definitions, and some talk about what they have to do with nonbinary people.
Androphilia is a romantic or sexual orientation in which one feels attraction to men or masculinity, regardless of one’s own gender identity.”LGBTQ Terms.”
Asexuality is a sexual orientation characterized by lack of sexual attraction. This is often accompanied by low or absent interest in sexual activity. Asexuality is distinct from abstention from sexual activity and from celibacy, which are behavioral and generally motivated by factors such as an individual’s personal or religious beliefs. Asexuals may have attraction sometimes but is not performed practically. Though asexuals lack in sexual attraction to any gender, may engage in romantic relationships. Some asexuals identify as MOGII. This can be because they feel that the category is appropriate because they experience discrimination for their sexuality like lesbian, gay, and bisexual people, because they experience romantic attraction to the same gender, or both.
Bisexuality is a sexual orientation in which a person feels sexual attraction to more than one gender of peoples sexuality. Some define this as attraction to women as well as men. Others define bisexuality as attraction to two genders of people: the same as one’s own gender, and different than one’s own gender. Others define bisexuality as attraction to people of any gender. What “bisexuality” means when nonbinary identities are taken into account is a matter of debate. Many people feel that “bi-” reinforces the gender binary, and erases nonbinary identities, preferring pansexual or polysexual. Others argue that “bisexual” was originally coined to describe a sexuality which included aspects of both heterosexuality and homosexuality, and that in a nonbinary context heterosexuality should be interpreted as inclusive of attraction to all other genders or sexes.
Demisexuality is a sexual orientation in which a person feels sexual attraction only to people they have formed a strong bond with, friends for example. It’s similer to, but not exactly the same as grey-sexuality.
Heterosexuality is a sexual orientation in which a person tends to feel sexual attraction only to people of a different gender identity than their own. For example, women who usually feel attracted only to men. This is heterosexuality even if one or both of the people are transgender, because this is based on gender identity rather than sex. Heterosexuality is often defined as attraction between persons of opposite gender
Heterosexuality. However, the idea “opposite gender” only makes sense within the gender binary, which sees all people as being either of only two genders, and that those two genders are supposedly opposites to each other. What “heterosexuality” means when nonbinary identities are taken into account is not agreed upon. By its etymology, it could imply “other” or “different” gender. In that case, a heterosexual nonbinary person could mean one who feels attraction to one gender other than nonbinary, to both binary genders, or to all genders other than their exact own. Nevertheless, heterosexuality is often assumed to refer to attraction between men and women only, even when nonbinary identities are acknowledged. This can cause distress to nonbinary people in a relationship and their partners as they struggle to find a labels for themselves. The question of whether a nonbinary person can identify as heterosexual– and how exactly that person defines their heterosexuality– is up to that individual person.
Gynephilia is a romantic or sexual orientation in which a person feels attraction to women or femininity.”LGBTQ Terms.” ”Neutrois.com.”
Homosexuality is a sexual orientation in which a person feels sexual attraction only to people of the same gender as one’s self. Nonbinary people who are only attracted to other nonbinary people can call themselves homosexual.
People who identify as gay men have a male gender identity, and are attracted only to men. This word is applicable regardless of whether one or both people involved are cisgender men or transgender men.
People who identify as lesbians have a female gender identity, and are attracted only to women. This word is applicable regardless of whether one or both people involved are cisgender women or transgender women.
Pansexuality is a sexual orientation that involves sexual attraction to people of all Gender|genders. Pansexuals are attracted to all types of people. They are gender-blind, asserting that gender is insignificant or irrelevant in determining whether they will be sexually attracted to others. Some people prefer to call themselves ‘pansexual’ rather than bisexuality|bisexual because of the latter term’s Gender binary|binary implications.
Polysexuality is a sexual orientation with sexual attraction to several Gender|genders of people. Polysexuals are attracted towards two or more genders, but not all (as in pansexuality) and not just both Gender binary|binary genders (as in some understandings of bisexuality). Not to be confused with polyamory, which is about having more than one partner at the same time.
Skoliosexuality, or ceterosexuality, means a sexual orientation in which a person feels sexual attraction to nonbinary people, and perhaps other kinds of transgender people as well. Jack Molay. “Transgender and transsexual glossary.” January 25, 2010. Some believe the term is only to be used by non-binary people, though it was coined in the context of binary people’s attraction to non-binary people. People who are attracted to other non-binary people may also use the term homosexual/homoromantic.
Due to a somewhat problematic etymology (skolio- comes from the Greek for “crooked”), some prefer to use the term ceterosexual, from Latin “cetera”, meaning “other”.
“LGBTQ Terms.” Neutrois.com. 
Jillian Cottle, “Hallelujah, it’s raining labels.”  http://en.wikipedia.org/wiki/Bisexuality
“LGBTQ Terms.” Neutrois.com.  http://en.wikipedia.org/wiki/Homosexuality
Jack Molay. “Transgender and transsexual glossary.” January 25, 2010.  http://nelde.deviantart.com/art/Sexual-Attraction-v2-180255547