Some strings you can shove into your application and see if you at least sort of handle Unicode correctly. For example, if you have a form which stores a text value in a database and then shows it later on a webpage, you can try to stick these in the form and see if they come out correctly in the other end.
- IÃ±tÃ«rnÃ¢tiÃ´nÃ liÅ¾Ã¦tiÃ¸n
First one includes many non-ascii characters. Second one starts with a multi-byte character.