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"I wanted to live no longer in that way" is grammatically correct. It means that you wanted to stop living in that way. If you expressed it as, "I no longer wanted to live in that way" it would mean that you no longer wanted that lifestyle. They are not exactly the same thought, but are very close: wanting to stop vs. stop wanting.
"I won't to live no longer in that way." Understandable, but incorrect.
"I didn't want to live no longer in that way." Wrong only because of the double negative. If you eliminate the first negative, that changes the first part to "I wanted..." If you eliminate the second negative, it changes to, "I didn't want to live any longer in that way." The difference between the two expressions is the same as above.