How can I type greek letters and mathematical equations into Evernote or any other OSX application?
Some might be available on your keyboard. Some might need to be inserted e.g. using Character Viewer.
Open System Preferences » Keyboard and check Show Keyboard & Character Viewer in menu bar.
You'll have a new status item to the right of the menu bar. From there, you can open the following:
Keyboard Viewer lets you see all the characters you can press using your current keyboard layout. Press modifier keys (option and/or shift) to see which characters you type when these modifier keys are pressed. Pressing
wwhile holding down option results in ∑ for me.
Character Viewer shows you all (?) characters available on your system. Select a character and click Insert, or double-click the character to insert it in your current text box.
If you have the Input Sources menu item in your menu bar, you can switch to a Greek keyboard layout. Then, you can just type without the Option key and you have access to the full alphabet.
Depending on the complexity of your equations it might also be an idea to have a look at LaTeX and in specific the free application LaTeXiT which can provide a system-wide shortcut (via the "services" menu) to typeset formulas though LaTeX and insert them e.g. as a PDF.
This has been a lifesaver for me when I had to typeset sophisticated equations into Keynote and PowerPoint presentations!
CajunLuke mentioned the input sources menu. Once you've selected the Greek keyboard in that menu, you can go to the preferences screen Keyboard>Shortcuts and assign a custom shortcut to switch input sources. It makes throwing a few greek letters into a sentence very quick and easy, once you've learned which keys map to which characters -- no need to open a viewer window or bring in the mouse. Just hit the shortcut, type in Greek, and hit it again to switch back.
However, be careful to make your shortcut a non-letter key (e.g., ctrl-shift-space). If you use a letter, it will be recognized when you switch from your normal language to Greek, but it won't be recognized when you want to switch back.