It’s a simplistic question, possibly even naive. Put it to a chemical engineer or a materials scientist, and she or he will almost certainly not come back with a single answer, but with (at least) two questions:

1. What do you mean by “plastic?” Do thermosetting materials like epoxy count? What about polymers that are reinforced with glass or carbon fiber infill?
2. What do you mean by “strong?” Are you talking about wear resistance? Compressive or tensile strength? Temperature resistance? Chemical resistance?

But say you limit your question to thermoplastic materials that can be melted and molded, extruded, spun, and/or drawn into various shapes. And that you exclude composite materials of any kind—just pure polymers without any reinforcement or infill.

Given those answers to question 1, a single material begins to stand out almost regardless of how you answer question 2.

That material is polybenzimidazole (PBI), marketed as a bulk polymer under the trade name Celazole. It is commonly reported to have the highest compressive strength of any unfilled plastic material, and also has the highest tensile strength, highest shear strength, and highest Rockwell hardness rating of any plastic that I have been able to find. It maintains its mechanical properties at high temperatures better than any other unreinforced polymer, and can reportedly survive short-term exposure to 1400°F, which is 200° above the melting point of aluminum. Phrases like “the highest performing engineering thermoplastic available today” are commonly used to describe Celazole in plastics industry literature.

NASA identifies PBI as a space program spinoff technology, and maintains an informative page describing its history, which, in fiber form, includes astronaut flight suits used on Apollo, Skylab, and numerous space shuttle missions.