Is there only in string in a quark or there many strings in each quark?

I'm not sure what strings you're referring to here. There are hadronic strings and superstrings.

Hadronic strings are a model to represent bound states of quarks joined by gluons (making up the body of the string). It takes at least two quarks to make a hadronic string.

Or --most likely-- you mean superstring theory (really tiny strings of Planck size). Then every elementary particle (electrons, quarks, photons...) would be a string. As a quark is, as far as we know, elementary (point-like, no internal structure), every quark would be a string within the framework we call superstring theory.

So a proton or neutron would each be 3 superstrings since each quark is a string?

Superstring theory purports to generalise the standard model. In the SM neutrons and protons, as well as mesons, are not elementary, but aggregates of quarks and gluons. So strings would correspond to quarks, gauge bosons (photons, W, Z and the graviton). 

Does one quark contain only one string according to super string theory?

Does an electron or a photon each contain only one string according to super string theory?

In Superstring theory, all fundamental fermions  ( particles ) and bosons ( forces ) are the result of differing vibrational frequencies of even more fundamental, Planck scale, supersymmetric 'strings'.

A composite particle, such as a neutron, would be the result of the vibrational interactions of the constituent quark/gluon strings.

A more generalized version, M Theory, and 'branes', considers the implications of some strings being a 'closed loop' and some 'open ended'.

Edited August 22, 20223 yr by MigL

What I am wondering is if one quark is equal to one super string.

In this model, every fundamental fermion or boson has an associated string vibration.
Not all particles are fundamental; some are composite.

You are trying to get a very simplistic understanding of a very complex subject; not going to happen.

Start here      Superstring theory - Wikipedia