A quick correction: transgendered does not refer to
sexual orientation. More like sexual expression, however
that term is problematic due to confusions with sexuality and that
sort of expression.
Transgender refers to what gender a person chooses to express
themselves as (regardless of biological sex as indicated by the
XX/XY chromosomes, though this is sometimes complicated in
individuals who have chromosomes of both sexes or whose DNA has
expressed different genetalia than their chromosones would
normally be expected to). For example someone who may have
been identified at birth as a female may choose to express as a
male but may find either males or females attractive for their
sexual partners. Now which of these encounters counts as
"homosexual" in nature is generally down to how accepting of
transgenderism a person is; personally I feel that a person who
expresses as a man who is with a person who expresses as a woman
is straight, and someone who presents as female and prefers to be
with other women is gay. Some people, unable to let go of
how they feel "sex"/"gender" is assigned (frequently based on
genealia rather than chromosomes - mostly because it's hard to
test folks DNA but easy to make a judgment based on more obvious
external fleshy bits) will consider a person they identify as a
"woman living as a man" (rather than a simply accepting them as a
man) having sex with a woman as homosexual in nature, however this
is discouraged as transphobic.
Sexual orientation refers to things like straight, gay,
bisexual, pansexual, asexual, etc.
Transgenderism uses different terms like cis, transgendered
man, transgendered woman, trans man, trans woman, FTM, MTF, etc.
Blenster