I refinance a house with a friend I had a falling out with, he owes me $20,000 and is refinancing again to get me off title. How can I get my money back ?

He said I will pay a lot of taxes if my name is on the closing statement 

GET A LAWYER!

Even if you owed taxes (not much) would you rather pay  a small amount of tax, or never get any money.

You bought a house together, you want him to "buy you out" of your half.  You need your name off the title, off the mortgage, and you want your money.  If you sign a quit-claim deed to take your name off the title, without a check in hand, you won't have any leverage to force him to pay you.  You can get a real estate lawyer to protect you for $500-$750, which is less than 10% of your hoped-for profit.  Well worth it.

For taxes, you will owe capital gains tax but only on your gain.  Here's an example of how that works:

Suppose you bought the house for $100,000, you each put down $10,000 and had an $80,000 mortgage, and you are 50/50 owners.  Your "cost basis" in the house is $50,000.

The house is worth $120,000 today.  You will sell him your share for $60,000.  After paying off the old mortgage, he owes you $20,000, which is your share of the downpayment plus your share of the "gain" in value from the original purchase.

Since your cost for your share was $50,000 and your proceeds for your share were $60,000, you have a $10,000 capital gain.  You don't pay any tax on that capital gain as long as you lived in the house as your main home for at least 2 years, and you moved out less than 3 years ago.  If it was not your main residence, then capital gains tax is 15% for most people, as long as you owned the house more than 1 year.  15% of the gain would be $1500, plus another $500 for the lawyer, means you net $18,000.  Instead of getting whatever he feels like he can get away with after he owns the home free and clear.