I'm almost sure that i was able to access the website normally a few years ago..
You probably could.
Did they do any changes which rendered it inaccessible to Amiga browsers or what?
Er, it seems pretty obvious they did, right?
Are there any tricks to access it with these browsers?
There's probably not a lot you can do. The development pace of IBrowse and AWeb is embarrassingly slow, so it'll be years before they're up to 2008 standards. Make sure meta refresh and Javascript are enabled. Spoofing as Mozilla or IE might help. You might also have some luck playing with the HTML and/or Javascript tolerance in AWeb.
Even if you do get further though, don't expect it to look how it should, or even work. Yahoo mail "works" with IBrowse in that you can log in, but that's about it. The page looks horrendous and you can click on emails to read them, but none of the "Delete/Reply/etc." buttons work. Hotmail will probably be even worse due to its Microsoft background.
EDIT: I see you've got a PPC, so things might be better with Sputnik on MorphOS or OWB on OS4 - they're the best chance you have.