I'm assuming silica-based C18 as polymeric resins might swell with these solvents. Chloroform and other organic solvents won't hydrolyze the C18 and can be used to clean the columns.
You can run non-aqueous reverse phase, referenced in referenced in Practical HPLC Method Development,Snyder, Kirkland, Glajch, 2nd edition, p.267.
I have run non-aqueous reverse phase on flash columns using acetone, dichloromethane, and ethyl acetate.
Here are some app notes/posters I've done on the subject:
http://www.isco.com/WebProductFiles/App ... idants.pdf
http://www.isco.com/WebProductFiles/App ... ld_C18.pdf
In the interest of full disclosure, I work for Teledyne Isco.