What is the strongest theory in science?

Theories are just theories

"Theory" is the strongest possible statement in science. To be considered a theory, an explanation is backed up by heretofore indisputable facts. One of the tenets of scientific method is falsifiability: something is the best known working explanation until overwhelming evidence demonstrates otherwise.

Most people use "theory" when they really mean "hypothesis." In science, the two are not even close.

This is a misunderstanding of what "theory" means. Theories in science aren't "just theories". They're specific explanations of natural phenomena. There is no pathway in science for a theory to progress into a "fact", because that's just not what the term means. A fact is something that has specifically been observed, zero inference. It is a fact that this apple I dropped fell to the ground. It is a fact that Earth orbits the sun. It is a fact that the solar system orbits the centre of the Milky Way galaxy.

"Gravity", in itself, is not a theory. It's the name given to the observed phenomenon of objects attracting relative to their mass. A phenomenon that has been described by Newton's Law of Gravity, which tells us that the force of gravity is proportional to the M₁M₂/r² where M₁ and M₂ are the masses of the two objects (e.g. the Earth and my apple) and r is the distance between them. Newton's Law proves useful at small scales, but fails to explain some phenomena, which is why Newton's theory of gravitation, while it was extremely useful in its day, has since been replaced by the explanation of gravity within Einstein's general theory of relativity. A good theory should be testable, and a great way to test a theory is to predict something hitherto unobserved. General relativity predicted gravity could bend light even though light is massless and thus would not experience gravity under Newton's theory. This was confirmed during a solar eclipse just a few years after Einstein published the theory. And more recently scientists measures gravitational waves, another Einsteinian prediction.

But even Einstein's theory of relativity does not fully explain all observed gravitational behaviour. Many large galaxies rotate at speeds faster than would be expected based on their observed mass. This phenomenon has been named "dark matter". Multiple theories exist to try to explain dark matter. Some say it's a specific type of particle. Others say that gravity is wrong and should be modified. Dark matter is an evolving field of research where, unlike relativity, no one specific theory is yet accepted by the vast majority of researchers.

TL;DR: gravity is the name given to the observed phenomenon of objects attracting. Multiple theories of gravity have existed as more evidence is gathered. Today, Einstein's general theory of relativity is held as the best. But dark matter (a phenomenon) puts a spanner in the works of our understanding of gravity. There are multiple different theories to explain the phenomenon of dark matter, none is universally held.

A fact is something that has specifically been observed, zero inference. It is a fact that this apple I dropped fell to the ground. It is a fact that Earth orbits the sun. It is a fact that the solar system orbits the centre of the Milky Way galaxy.
I wouldn't even go that far. We didn't even know that galaxies existed as a concept until about 100 years ago, believing that spiral smudges we saw in the telescopes were just weird nearby nebulae. It was at the Great Debate of 1920 that the consensus shifted into believing in multiple galaxies spread across large distances. Galileo notably got into trouble for promoting the other mentioned theory. If you start calling these "facts", you yourself are giving into OP's world view that a theory becomes fact if it is strong enough.
- This. The concept of a "fact" doesn't work in science, because anything can theoretically be disproven.
  The main concept of science is that we observe things and infer models and rules. Since we do not observe rules but only infer them, all is a theory, which means "This is our currently best understanding of things. We treat them as if they were fact. But we also understand that our current understanding might not be perfect and thus we call things theories instead of facts."
  Calling something a "fact" means it's perfectly finished and there's nothing to add to it. That's inherently unscientific.
  Btw, when a theory is replaced, it's hardly ever replaced with something entirely different. Usually it's just expounding. Newton's physics remain valid in almost all situations, but Einstein's relativity fixes the edge cases where Newton doesn't work.
  Which is why when building a bridge you use Newton's physics to this day, and not Relativity (unless the bridge is moving at close to the speed of light).

Evolution? I don't think that has ever been successfully refuted.

Plate tectonics?

Yeah natural selection through heritable traits seems like almost tautological.

Anyone here going to start the hypotheses vs theory vs law discussion?

I think that's the whole post.

There are many physics theories that have not been contradicted by serious evidence to the contrary. That's a 'strong' theory.

In the past century, quantum mechanics ... while "noone understands it" (Feynman) has led to many inventions (and much confusion). Einstein's relativity has stood up well to many, many tests. If you go back to 'classical physics', Maxwell's (more understandable) conclusions about electromagnetism have never been off the mark.

Lift. I love that some people still argue over how it works and the oversimplified explanation we give kids is digestable, but completely wrong.

https://www.scientificamerican.com/video/no-one-can-explain-why-planes-stay-in-the-air/

https://aerospaceamerica.aiaa.org/departments/so-you-think-you-know-lift-better-read-this/

Theory of Gravity - Has lots of weight behind it. Something everyone can demonstrate for themselves, seems like a highly likely theory

No offence mate, but given this statement and the question in the op you should go back to the very basics, your understanding of science in general is seriously lacking.
'Theory', as in 'theory of relativity' or 'theory of evolution' for example, doesn't means 'conjecture', it means 'model'. It's a framework that let us understand some phenomenon. Relativity for example is not very complete, it works perfectly in a macro scale but breaks at a subatomic level, for that we have the standard model. Evolution, tho, doesn't break at all. A basic requirement for a proper theory is being able to make accurate predictions on its domain: with relativity we can predict how planets behave for example, we'll need the standard model to do that for an electron.
Out of the four fundamental forces gravity is the less well understood.
- Most often if a theory gets replaced, it actually gets expounded upon, fixing the edge cases where the old theory didn't work.
  Newton works at "normal speeds" but doesn't work when things move really fast, so Einstein fixed that with relativity, and quantum mechanics expounded on Einstein.
  But the older theories remain valid in their domains.
  That's why when building a bridge you use Newton and not relativity or quantum mechanics.
  Neither Newton nor Relativity were wrong. They just don't explain absolutely everything.
Technically gravity has mass behind it
Except its not complete, right? There are contradictions that need solving.
- Not really contradictions, there are those behaviours which you describe (i.e. speeds at the outer regions if galaxies faster than originally expected) and from those we come to things such as dark matter which describe these, but we don't yet know what they are.
  It might be that the theory needs to be changed if there is no such thing as dark matter and it Is jnice calculation trick that actually mean something elsr in the real world, but as of right now it describes most things well.
  Alas, there is the disconnect between different theories that don't work together (see Gravity and Quantum mechanics) or only on different scales
- Ohh? I haven't been keeping up with gravity. What are these contradictions?

gravity

dark energy would like a word
- wouldnt the strong force qualify also

The theory that something exists. Lots of evidence for that one.

But what is "something"?
- Take your pick. The world around you, your self, your own experience. Even if everything you observe is a simulation, or figment of your imagination, that still proves that something exists.