If you have a table of codes like this one,
http://www.asciitable.com/
you can display the character by typing in the number of the character while holding down the ALT key. For example, if I press and hold ALT while typing 234 235 236 237 238, I get Ωδ∞φε. You can also copy and paste characters from other sources.
Ah I see. Then I would say the problem is almost certainly one of encoding, and specifically what grmcdorman cites.
By the way, just to be pedantic: those characters aren't ASCII. ASCII is only the first 96 characters (ordinals 32 through 127, basically the characters on a US keyboard: letters, digits, and punctuation). Characters above 128 vary; the three most common 8-bit character sets are ISO LATIN-1 (ISO-8859-1), the Windows character set (Windows-1252), and UTF-8. Given that Bob B. is trying to enter Greek characters, he probably expects Latin 1 or UTF-8.
My Web developer tools in Firefox report this site as UTF-8, by the way.
/pedant
Getting in the spirit of things:
[pedant]Pretty much all the common encodings (including UTF-8) agree on the meanings of up to 127; from 128 to 255 is encoding-specific. Many old systems used the eighth bit for parity or similar purposes. When that stopped being cool and trendy, the eighth bit became available to convey non-redundant information, and was frequently used to encode characters commonly used in non-English languages, which were not included in the lower 128. But there are too many Greek, Russian, Hebrew, etc. letters, to fit in the range 128-255. As a result, in computer in Israel may well use the range 128-255 to use different characters than a computer in Russia, and opening a document produced in one country on a computer in another may result in the display of gibberish, if the software on the target computer is not capable of identifying (or being told) and using the correct encoding.
So I would think that what is happening on the other board is, you are entering characters using one encoding, and it displays them using a different encoding, the result of which will be perfectly OK for characters up to 127, but gibberish after that. So options are
a) change the default encoding on the other board to what you want - would have to be something the board software can do, and the board administrator would agree to.
b) use the existing default encoding on the other board - the default encoding would have to support the characters you want, and you would have to cope with entering the same character one way on that board, and a different way on other boards.
c) change the encoding on a message-by-message basis - I don't know whether this is possible, but maybe there is a bbcode or something of the like that does it.
Seems to me the world is moving towards UTF-8 (as per above, a 1-4 byte encoding, in which certain bytes indicate that this character is continued into the next byte, but coincides with ASCII up to 127), but maybe there are good reasons to stick with other encodings.
[/pedant]