Let's say I send some compatible ERC-20 tokens to myetherwallet (not ether). Two years later, the developers/miners/company that control the token decides to move from the ethereum blockchain to their own one that they just created. In this scenario, what would happen to the tokens in myetherwallet?
It depends on what the company decides to do and the nature of the token. If ether is tied up in the token (e.g., like the DAO), then it’s complicated.
If the tokens aren’t controlling the amount of eth in a contract (cf. the market cap of the token), it’s really dependent on the company. This is the case with most tokens I’m aware of. Indeed, aside from the DAO which has no owner (just a pwner) and its ilk, I think pretty much any other mode is either a scam or operating suboptimally (see my posts here for an example). Such tokens are largely symbolic like fiat currency. When European countries switched from their local state currencies (e.g. the lira and franc), they provided a transition to the euro. Contrast this with the wildcat banks of the US where the dollars they issued became worthless if no one assumes the liability and they closed up shop. This is not unlike the value of gift cards for a company that gets bought out by another company or goes bankrupt. You might just end up with a bunch of worthless gift cards (tokens).
We say that smart contracts are trustless, but when you’re dealing with a contract whose value derived from a person (incl. companies which are legal persons), the contract is only worth as much as you can trust the person you’re dealing with.
This depends entirely on the token's contract. If the contract allows some privileged account (e.g. an "owner") to change people's balances or destroy the entire contract, then you are at the mercy of that privileged account and what it decides to do.
Most tokens, however, have no such thing as a privileged account. In such a contract, it doesn't matter what the person who created the contract wants; they cannot change your token balance.
The only way to answer this for a particular token is to read the source code for that token.