How possible it is will depend on how familiar you are with tweaking Windows. Let me start by saying I do not recommend what you are trying to do nor will Oracle Support likely assist you with such a configuration ("not supported"). Further, understand that using more than one version at a time will not likely be possible. If your goal is to just use the Builders (don't run any forms), this might be easier to accomplish.
So, your v6 installation stopped working. Well this is likely because each time you install something the system PATH is updated. Likely the first entry in PATH now points to the v11 directories. This will cause older versions to fail. Conversely, if you put the v11 entries last, this will cause it to fail.
The only way to really make this work would be to remove all of the Oracle references from the system settings and start all needed processes manually via a script that sets up the environment as needed. The only other option that I could think of is to manually change the system PATH, CLASSPATH, and ORACLE_HOME prior to using each version. Again, trying to use more than one version at a time will not likely be easy.
Yes, all three can co-exist on the same Windows box. I currently have Oracle Froms 6i, 10g R2 and 11g R2 installed on the same workstation. The Form Builders work fine, however if you plan on running a form from the Forms Builder, you will have conflicts between the OC4J (Forms 10g) and the WebLogic server (Forms 11g). I was able to work-around these conflicts by altering the System Path and make sure the Forms 10g entries appear before the 11g entries when I need to run a form from the 10g Forms Builder. Conversely, you have to make sure the 11g entries appear before the 10g entries when running a form from the 11g Forms Builder.
I did see a thread where someone mentioned they were able to make both work without having to alter the System Path, but I've been unable to find this thread again to test their solution. You could search for this thread if you don't want to alter the system path each time.
Forms 6i doesn't conflict because it uses the Forms Runtime instead of an Application Server to run a form from the Forms Builder.
I mean, what variables in particular need to be set?.
- not sure what to put on that script
Please also notice my Windows is 64 bit and my 11g installation is 32 bit. This means, variables are located on HKEY_LOCAL_MACHINE -> SOFTWARE -> Wow6432Node -> ORACLE. The main setting are for my 6i installation which is work fine, i have two additional key, one for my 10g installation and one form my 11g.