Unable to open multiple documents in Word or Pages using Command-O in OS X 10.9.4
This seems to be a bug in either Word or the OS. I've seen this behavior since Lion at least, and have been dealing with it myself just today. Have you tried re-associating file types for Word documents? After setting .doc and .docx files to open in Word by default (Get Info --> Open with --> select or re-select Word, then click Change All), I can launch multiple files again without any problems. It may not be a permanent fix, but it works for me.

If you hadn't mentioned that this affects Pages as well I would blame MS Word, but given this, and that reassociating files seems to help, it sounds like an issue with the way the OS is handling these file types.