Œ and œ can be inputted using the US International keyboard with the combination AltGr+X or AltGr+x respectively.
As a comment reports, the above quotation was removed from the Wikipedia article on 25 July 2012. It is not clear whether AltGr+x=œ was always untrue or whether the behaviour changed to accommodate the use of Alt+x to convert preceding four hex characters to a single Unicode character.
Some applications provide support for entry of characters beyond the simple accented Latin-1 characters.
In Microsoft Word, "œ" is entered using ctrl + shift + & then o in quick succession. Some word processors such as MS Word can automatically correct French words like soeur to sœur, but in most other applications (e.g. an instant messenger, or a browser) the word will not be corrected.
In Vim (text editor), use Ctrl-K then 'o' then 'e' in succession. (or 'O' and 'E' for upper-case).
Vim has a very good and extensible set of digraphs. You can also use it as a text editor in web-browsers by means of the ItsAllText plugin or TextAreaConnect, thus bringing digraphs to web-applications.
Quotes are from Wikipedia