He's wearing sleeve garters. Popular in the late 1900s when mens' shirts came ready made in very few sizes and so had long sleeves so they'd fit the most people possible. There are several things wrong with Akio wearing them.

1. He's fucking tall, he wouldn't need them.
2. They were also associated more with working classes or the not-super-rich, who of course could afford tailoring. The popular stereotypes you'd see wearing them now are bartenders and gamblers and such from the era.
3. His are gold. WTF.

Something the wiki doesn't mention is sleeve garters, along with suspenders, and other men's functional wear that isn't necessary anymore, have actually tested among women as equivalent to lingerie in that they tend to uh...spark the imagination.

They make him look like a riverboat gambler or some other kind of hustler. They also look like manacles and creates some kind of continuity with Anthy's ankle bracelet (from the last episode).

Well, so I didn't know the history of those armbands before... When I saw them first, they looked like chains to me - a sign that even Akio is somehow trapped, in his case it's both Ohtori Academy (is he any longer able to live outside? Without his smaller and bigger plots and feel of control?) and his own past.

Everything old is new again.

I originally took from them the same thing you did, Enea, and I suspect that's what the design is meant to imply. That and the whole working man's style thing--for all his expensive cars and such, Akio does a fairly piss poor job presenting himself as obnoxiously rich. He carries the hallmarks of, if any group, the nouveau riche. Expensive gadgets, expensive accessories, and a lot of flash. Very much the opposite of the demure and understated elegance that would be expected of old money.

There's also that his armbands echo the gold armband Anthy wears in the flashbacks, which could be also part of that depiction of him as the one trapped now. The loose red shirt would also be an echo of her very baggy little red number. Almost like he wants to 'accidentally' remind her of who she was at that time, trapped, oppressed, but strong.

As for Japan, I've never seen a bartender of any status depicted in Japanese media that didn't have the armbands. It's a fashion statement they seem very fond of, which makes sense since it's from the Prohibition era that lends a lot to their current cocktail culture.

What makes you think they're oversized?