You can key unicode hex input directly into any application in Mac OS X. I’ll explain how, assuming that you are using default keyboard settings.
First, I’ll briefly review how to produce an accented letter in a western language: In the normal, default U.S. or Canadian English situation, holding option down while tapping certain keys (e or i or u, for example) remembers an accent (such as ´ or ˆ or ¨ respectively) but makes no mark. The immediately following keystroke (typically a vowel) produces an accented letter (providing the particular letter keyed is capable of taking the particular accent).
Perhaps you know the Unicode code point for a particular character, such as U+03B1 for Greek lowercase alpha (α). The Unicode Hex Input method allows keying such a code directly. First, make sure that Unicode Hex Input is enabled. Under the Apple menu (at the left of the menu bar), choose System Preferences…, then choose Keyboard. Make sure there’s a check in the box to the left of “Show Keyboard & Character Viewers in menu bar”: This will display a flag (or flag-like) icon near the right-hand end of your menubar. Then choose Input Sources… to access the preferences for Language & Text. Near the bottom of the (long) scrolling list, place a check next to Unicode Hex Input, and at the bottom right, make sure there's a check next to “Show Input menu in menu bar.” Close the System Preferences window. Now, return to the application you're interested in, and look at the right end of the menu bar for a flag. Pull down that menu; Unicode Hex Input will now be one of the choices.
Choosing the Unicode Hex Input method alters the behaviour of the “option” key. To place U+03B1 into your document, hold down the option key and – while holding it down – tap the four keys 0, 3, b, and 1 in sequence. On pressing the last of the four, the character α appears; you can then release the option key. To return to the normal option-key behaviour, access the “flag” menu and choose your usual input method.
With default keyboard settings, you can now switch input methods by holding Command (⌘), tapping the spacebar one or more times until the desired method is selected, then releasing the Command key.