This week's book giveaway is in the OCAJP forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide 1Z0-808 and have Jeanne Boyarsky & Scott Selikoff on-line! See this thread for details.
I would normally recommend including the properties files in the EAR file unless you need to change a file and don't want the hassle of rebuilding and redeploying the EAR. This could apply to a logger or configuration file. (Having said that, it may be possible to deploy an exploded directory - as you can with WebLogic Server - in which case you can edit the properties file in situ.)
There are several ways of achieving this. One way is place your JAR file containing the properties files anywhere in the EAR (say the root) and refer to it in the Manifest Class-Path of the J2EE modules that need access.