Getting from client/server based 4GLs and databases where the 4GL is tightly linked to the database to Oracle and the cloud is not easy. The least risky and expensive option (in the short term) is to use the Progress OpenEdge DataServer for Oracle:
Progress OpenEdge DataServer
This eliminates the need to have to migrate the Progress 4GL to Java/J2EE.
The database can be migrated using SQLWays Ispirer:
Ispirer SQLWays ProgressDB migrations tool

The Progress 4GL can remain as is. In order to get the application on the cloud there are a few approaches:
1. VDI - Virtual Desktop is a way to put all of the users desktop in a centralized environment off the desktop. This is great in cases where it is just not one client/server application that the user needs access too. In many cases, users will utilize MS Access, MS Excel, Crystal Reports and other tools to get at the Progress DB and other centralized databases. Vmware's acquistion of Wanova shows how VDI is growing in usage. Citrix is the 800 pound gorilla in the VDI space with Citrix WinFrame (now called XenDesktop). Oracle offers a VDI solution that Oracle picked up when it acquired Sun.
2. Hypervisor Server Virtualization - Of course you can place applications written in client/server languages like Progress 4GL buy using server virtualization from Oracle, VMWare, Microsoft, Citrix and others.
3. Microsoft Remote Desktop Services (aka: Terminal Services Client)
The entire idea is to eliminate all the client/server desktop devices and connections which require desktop software and database drivers. A solution to removing database drivers from the desktop is to use DataDirect SQLLink