You would be better off upgrading your internal hdd/ssd and replacing it with a decent sized hdd. External storage is best used for backups and user data.
It is possible to merge the root file system and spread it between two or more storage devices but this not a good idea with removable storage as the system may fail to boot properly when the removable storage is not present.
If you have Wine installed, you can run some of the Portable Apps
Portable Apps software from your external drive. (but not all will run well under Wine)
Some Java based apps also have stand-alone versions. (Sweethome3D for example)(Sweethome3D for example)
Generally, there is no simple 'plug&play' solution to what you're asking for.
Try experimenting with various software and see what you can accomplish.