I understand how particles with certain masses can form to make atoms, which create rigidity in objects due to Pauli's Exclusion Principle and what have you. These particles actually have mass and to a certain extent clearly would produce rigidity in objects.
Do you understand what rigidity is ? I would define it as the resistance of a solid to change, up to a dimensional length of 10^-8 cm. If you have an electron microscope you would see that there is some motion always happening at those lengths and nothing looks "rigid".
At those dimensions the basic fabric of nature, which is quantum mechanics, appears and terms like "rigidity" and "mass' have to be rethought for the microcosm. So the "particles" with "mass" making up atoms and the atoms making up solids have a different behavior/appearance in the small dimensions than the large dimensional objects they make up in aggregate.
A nucleus and its electrons are moving in a cloud of probabilities , described mathematically , and seen only in designed experiments. The collective behavior is what we observe macroscopically.
But how can particles as closed strings (which I assume would be massless, please correct me if I'm wrong) still produce rigid objects?
An elementary particle, when represented mathematically as the vibration of a closed string does have mass, but this mass is not the same as the one you measure macroscopically on a scale, it is the relativistic mass. It has charge and spin and all the quantum numbers that describe the particle. The string is a mathematical description of the known properties of elementary particles that is hoped to be more general then the Standard Model description, and will allow for predictions and the inclusion of gravity. In atomic dimensions it is indistinguishable from the point particle of normal quantum mechanical description, so the mass of an electron for example is the same whether you call it a string or a point particle.
One has to build knowledge of physics slowly and systematically, in order not to get side tracked and confused by terminology.