Due to the character composition table being hardcoded, the characters ō, Ō, ā
and Ā (upper and lower case "o" and "a" with macron) can't be input using the
composition method.

Characters such as ū, Ū, ē, Ē, ī and Ī can be entered using Alt Gr + - followed
by the letter without the macron, as expected. With the o and a however, the
resulting characters are:

Alt Gr + - followed by o = õ
Alt Gr + - followed by O = Õ
Alt Gr + - followed by a = ã
Alt Gr + - followed by A = Ã

Although it should be possible to enter these resulting characters—since they
are used a lot more often then the macron vowels—they are already available
through other combinations which seem much more suited for those characters:

Alt Gr + ~ followed by o = õ
Alt Gr + ~ followed by O = Õ
Alt Gr + ~ followed by a = ã
Alt Gr + ~ followed by A = Ã

So why are these (õ, Õ, ã and Ã) available through the "dash" key as well? The ũ
and Ũ character for example can only be input with the "tilde" key, are the õ
and ã different in some way?

I haven't been able to find a reason for this behaviour, although I expect a
good reason to exist. The characters that can't be entered now (especially the ō
and Ō) are used often (amongst others) by academics and students studying Japan
and the Japanese language in transcribing Japanese using the Hepburn system.

A possible solution to this problem might be the patch described in bug 155010.
That bug proposes an user configurable composition table.