There appear to be a few ways to get the unicode characters on a Mac. The first few don't appear to be what you want exactly, but included for completeness.
1) Make sure System Preferences->Keyboard "show keyboard & character viewers in menu bar" is selected. Then you can click on that (normally accessible via option+cmd+T, but not in eclipse) to get the Character Viewer. You can then double-click a special character you want and it should insert at cursor.
2) Under the default setup, you should be able to click Option + key to get an alternate character. Use the keyboard viewer from #1 to see what maps to what. Note you can switch to some more mappings using Shift at the same time. This will only get you a subset of unicode characters.
3) From here: Under System Preferences->Languages & Text, go to Input Sources tab. Select the Unicode Hex Input source. You may need to assign switching input sources (under System Prefs->Keyboard->Keyboard Shortcuts->Keyboard) to a hotkey combo (default probably conflicts with spotlight, so change to something else). After that, you should be able to use said hotkey combo to switch to the Unicode Input Source - in that mode, you can hold Option down and enter a hex 4-digit key code, which will result in the character being placed at cursor.