Replacing greek glyphs in math mode

In your lualatex example the \renewcommand{\rmdefault}{bodoni} won't work. It will look for an eu2bodoni.fd which doesn't exist. Switch to the font you want mathastext to pick up by using (as described in documentation) a suitable \setmainfont before loading mathattext.

Apart from this: The font selection depends a lot of the actual font. It is rather easy to replace the font for letters and numbers, but when it comes to symbols you need one or more fonts which contains them and you will perhaps have to adjust various fontdimens. If you really want to use another open type font for the symbols your best bet is at my opinion unicode-math, but it can't do wonders if a symbol doesn't exist:

\documentclass{article}
\usepackage{unicode-math}
\setmainfont{Arial}
\setmathfont{Arial}
\begin{document}
$ a = \sin{0} \int \boxtimes \mp$
\end{document}