If this is true then why does the strong force "pull" the particles together to make them stick or bind to each other? How does interaction between states ensure that the particles remain together in space?
Particles are quantum mechanical entities, i.e. obey the rules of quantum mechanics. Classical mechanics emerges from the underlying quantum mechanics for large distances and large masses, smoothly . Force is a classical concept that in the context of quantum mechanics becomes dp/dt, the transfer of momentum during a particle-particle interaction.
What makes particles stick together or repel each other depends on the sign of the various dp/dt components, interactions, entering the problem. See this answer as an example.
Once attracted particles may bind together in space ( and time) in quantum mechanical states that are stable energy levels. It is the reason the theory of quantum mechanics was developed, because of the stability of atoms atoms are at most metastable for classical electromagnetic solutions of the problem "electron around a proton".
Weak interactions' attraction or repulsion depend on the type of particles participating and their flavor, see the answer here to a similar question.