When most people think of orientation they think of sexual orientation but the reality is that it is more complicated than that. Who people are attracted to sexually is only one aspect of orientation there is also who people are attracted to romantically as well as what other people attribute your orientations to be. These different aspects line up in most people, though the attribution can be different for some who aren't heterosexual or obviously homosexual but for those who aren't of a 'mainstream' orientation or whose sexual and romantic orientation this aspect of who they are can be rendered invisible.
Sexual orientation can be divided into a number of categories, not all of which many people have heard of. The categories are hetero, homo, bi, pan, omni, a, demi, and sapio. Heterosexual people are those who are sexually attracted to people of the opposite sex (whatever that means, usually this is used for people in a binary-identification of sex or gender). This is also called androphilia when people don't want to attach a gender to the people involved. Homosexual people are those who are attracted to people of the same sex, this has the same binary implications as heterosexuality does. This is also called gynephilia for similar reasons to androphilia. Bisexuality is the last binary identification and is sexual attraction to 'both' genders.
Pansexual and omnisexual are sexual attraction to all genders and attraction that isn't based off gender respectively. These two orientations are often put together into the same category. Asexual people aren't sexually attracted to other people and demisexual people require a relationship before sexual attraction occurs. Sapiosexual people are attracted to intelligence without regards for gender or sex. Romantic attraction has the same categories as sexual attraction but deals with who a person is attracted to have a romantic relationship with.
Orientation attribution is what other people assume your sexual and romantic attribution. Usually people assume that these two attributes match but that isn't always the case. Unless yours happen to not match however there is a distinct possibility that you have never realized that they are two different orientations. People who are assumed to be heterosexual/romantic are given cis privilege even if they aren't hetero, even the assumption of homosexuality and bisexuality give a person cis privilege that the other orientations don't get. Far too often a person who is of a non-binary orientation is rendered invisible, even in human sexuality classes where the professor should know better.
One thing that happens far too often, especially in homosexual communities is the assumption that orientation must be stable. A person changing their orientation is seen as a traitor to the community and even if that doesn't occur in many cases they aren't welcomed back into the community to the extent that they were previously. The reality however is that all orientations have some degree of fluidity. While many people have relatively stable orientations, like with gender, orientation can have a small, moderate or high level of fluidity. These fluctuations may just be for one person, or just every so often but in others there is a significantly greater level of fluctuation. Maybe the person identifies as homoflexible – a designation that says that the person is mainly homosexual but isn't entirely objecting to the possibility of an attraction to a person of another gender.
There is a lot of research into sexual orientation already, though most of it is on hetero, homo, and bi sexual people. Research is minimal on asexuals, and nearly non-existent for the other orientations. I think the best way to do this research would be to do a survey of people to find their sexual and romantic orientations both via self report and adaptations of scales previously used to detect sexual orientation. A lot of these scales can easily be adapted for use on looking at romantic orientation as well.
Looking into orientation attribution would be done in the same way as the other attributions; asking a group of people to identify peoples orientation based off of a profile of the person. In this case a written case report of various people from a variety of sexual and romantic orientations and having the people involved write down what they think the case studies orientations are. Another way to do this would be to have a staged video of a dance or party then have the participants watch and determine what the people at the event have for orientation.
As with the other categories that deal with fluidity sexual and romantic orientation fluidity can be measured retrospectively via a survey asking people how their orientations have changed over time. This can then branch out into a more in-depth set of research where people journal their orientation perhaps on a monthly basis over the course of time to see if it changes. The longitudinal study would have to take place over a number of years so that there would be a complete picture of peoples fluidity. This would be the most difficult to develop a measure to test because orientation fluidity isn't socially acceptable in may areas and many people have a goal of finding one person to settle down with and thus don't do a lot of changing of orientation after that.
As for practical uses of this I think that the best place this information can be used would be in couples therapy to establish a background on the clients. I am not sure that this orientation information alone would have much practical use beyond that but used in suite with the other areas of sexuality and gender this can give a clinician working with a person a lot of information to go on when they are assessing someone for gender or sexuality related problems. Establishing a clear baseline that doesn't deny the person's identity is vital so that a good therapeutic outcome can be reached.