For the Alt 164 kind of code, you use the numeric keypad; but for the
Unicode codes like 03A6, Alt-X, you use the regular number keys. (Just
type the four characters, then Alt-X.) Does that make it work?
You assign your own shortcut to any character by going to Insert
Symbol, choose the character you want, and at the bottom is a
"Shortcut" button. Click that, type the code you want to use, click
Assign (and a panel opens where you can check whether that code is
used for something else), and then Close. (If the dropdown at the top
left is set to a particular font instead of "(normal font)" at the top
of the list, your shortcut will always insert the character in that
particular font, no matter what font the surrounding text is.)
To find the Greek letters, be sure the code type is set to Unicode
near the bottom right, and at the top right choose Greek from the
dropdown. To avoid conflicts with existing keyboard shortcuts, I'd
recommend using Ctrl-Alt-G, f for Phi (and Ctrl-Alt-G, Shift-F for
capital Phi). You could then do any other Greek letters you might need
with Ctrl-Alt-G as the "prefix."