Edgeworth is the only one I play, so let's go with him!
The important part of Edgeworth's sexuality isn't what sex/gender he's interested in (more on that later), but how he goes about it
In canon, he's shown to be completely oblivious (or at least, disinterested) to sex and romance
Granted, this is mostly in relation to female characters, but since no male characters really make a move on him, his feelings on dudes will
what aa games are you playing
because phoenix is all over him ok
BUT EVEN THEN IT FLIES OVER HIS HEAD
"What? Someone cares about me on a deep, personal level? Poppycock"
hush, you
Now, this is a good argument for him being asexual. HOWEVER
/stays in this plurk and derails it forever
Edgeworth is also... pretty stunted when it comes to normal social skills
He can be pretty charismatic in the courtroom and with professional matters
but when it comes to making personal connections, he's just not very experienced
plus, he's also a perfectionist, which would give him a lot of anxiety if he was interested in sex/romance
But basically, I'm of the mind that you can BS almost anything for his sexuality, so long as you keep the following in mind:
his dedication to his cases, investigation, the law, and, after he reforms himself, the search for truth and justice, will always come first
sex/romance just won't be a big priority in his life, if only because of his work and his goals
So, you could play him asexual, you could play him gay, you could play him as straight/bi/pan but awkward around women...
hell, for all we know, he could be one of those "3D IS DISGUSTING, 2D IS SUPERIOR" nerds
as for me, how I play him depends on the game/plot I'm in, who I'm playing him against, etc etc
For example: I play him as gay in DV, but I've also played him as asexual, and I've also played him as bi in the past