I've tried applications like Mojo and portableapps creator but either it doesn't work or I need Administrative rights (Mojo).
How can I get a simple install app to work on my USB without being an Administrator?
Most applications require administrative privileges not only to write to the disk (in your case USB) but also:
All these require that you are an Admin on the PC you install it or run it(the App). Hence even if you install an app on the USB which is not a portable app, it may not work properly/at all on other PCs.
A truly portable app is one which does not require any of the above & also writes user prefeences in an *.ini or *.xml file.
Good portable (portable means one need not install itbut may require admin rights) applications for USB can be found at PortableApps. (Freeware) For setting up PortableApps on your USB you may need Admin rights (not likely), but running it does not (Depends if you are in corporate environment, Group Policies may prevent application execution from USB).
Also you can directly run the applications (like Firefox Portable, Notepad++ Portable) available on PortableApps site without installing them.
To make an application portable, the most effective way is VMware ThinApp but it's a 5000$ license.
If you're not rich enough you can struggle with this, alpha stage and not anymore developed, freeware: JauntPE.
All other solutions I found don't really make application portable, they just remove registry and files after the application use... So they are not usable without administrative rights.
So, without administrative rights, I think we are limited to use applications natively developed to be portable...
Notable exception for all these solutions: