What is the PGP Web of Trust Strongset? I understand that it is a system that "establishes the authenticity of the binding between public keys and their owners", but how does one join this web of trust? Do you have to physically meet one of the existing members, and they can get you in?
The web of trust is no longer active. It was removed in GPG version 2.2.17.

The way it worked was that people would meet in person and sign each other's keys, then upload those keys and signatures to a network of "keyservers". Or maybe they'd just verify that email could be delivered to the other person. Or sign whatever they were asked to with no verification. In theory you could likely find some path of signatures back to a signature by someone you trust, thereby letting you establish a chain of authentication to believe that a key belonged to a given person, as long as everyone in the chain always actually did verification of all the keys they signed. In practice that was rarely done, people just trusted keys identity on first use.

Then in June 2016 the keyserver network was attacked in a way that fundamentally broke the whole thing. Anyone can add a signature attesting that a key in the keyserver is valid for the name it claims to be for. Anyone can add 150,000 such signatures. GPG breaks horribly whenever a key with more than about 150,000 signatures is used, or is anywhere in the chain of trust needed to verify another key. Someone signed a couple of popularly-used keys 150,000 times each, thus breaking GPG for everyone who was actually trying to use the Web of Trust. 

So the Web of Trust was removed, the keyserver network is useless, and nobody really cares because no one really relied on it anyway.

And this is all without mentioning all the other massive vulnerabilities in the design and implementation of PGP/GPG, like its default to 1024-bit DSA keys with SHA-1 hashes (both broken), its common doomed attempts to encrypt email, lack of forward secrecy, use of RSA for encrypting, extremely complicated interface, long-lived identity keys, ease of creating colliding key fingerprints, etc, etc. It's a long, long list and not entirely on-topic to this answer.