Creating odd harmonics without the fundamental
Im looking for a mathematical function which can recreate any fundamentals odd harmonics, in a multitone input...


(emphasis by me)

What you ask for is not possible. If you demand multiple tones and complex tones as they appear in music, then your problem leads to a conflict. A complex tone comes with overtones. Even if you have a process that adds odd harmonics to each sinusoidal component, then the even overtones of the fundamental frequency will contribute even harmonics. That is because an odd number multiplied with an even number is again even.

So circumvent that, you would have to identify the fundamental frequency of complex tones first, leading you directly to the problem of polyphonic pitch detection which remains mostly unsolved.

Maybe you should explain what you're really trying to accomplish, as in what the application is that you have in mind. With that information it's quite likely that we can come up with a relaxed set of requirements that can actually be implemented.