may / might / might as well?

Let's look at all three choices to see what the sentences mean in each case.

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"Might as well":

Used to suggest doing something, often when there is nothing better to do. [Cambridge]

Now let's look at the sentences with "might as well":

You might as well get a taxi from the station. It'll be quicker than me coming in to get you.

This essentially means

Get a taxi because it will be faster than me picking you up.

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"May":

Used to ask or give permission. [Cambridge]

In our case, we are concerned with "giving" permission.

The sentences with "may" are:

You may get a taxi from the station. It'll be quicker than me coming in to get you.

and it means

I am allowing you to get a taxi because it is faster than me picking you up.

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"Might":

Used to express the possibility that something will happen or be done, or that something is true although not very likely. [Cambridge]

The sentences would be:

You might get a taxi from the station. It'll be quicker than me coming in to get you.

and mean

There is a chance that you will get a taxi. If you get one, it will be faster than me picking you up.

The sentence with "might" is unnatural; I would not recommend using "might" in this case.