Por eso, por lo tanto, así que

[poli]

Are these terms interchangeable? I find myself using por eso mostly.

[AngelicaDeAlquezar]

Yes, they are.
"Por lo tanto" is a bit more formal, I think

- Tembló anoche; por eso hoy no hay clases.
There was an earthquake last night, that's why there is no school today.
- Hace mucho calor; así que se me antoja un helado.
It's too hot; so I'm craving ice-cream.
- Ha estado lloviendo mucho; por lo tanto, todo está encharcado.
It has been raining a lot; therefore there are puddles everywhere.

[Tomisimo]

In my experience, por eso and por lo tanto are fairly interchangeable.

por eso == that's why (as an interjection, por eso == exactly)

por lo tanto == for this/that reason, because of this (slightly higher register than por eso)

así que == so