Pay is the most general of these three words. Employees who work in factories, etc. get their wages each week. Employees who work in offices or professional people such as teachers or doctors receive a salary that is paid each month, but is usually expressed as an annual figure.
A person's earnings are money that they have earned for doing a job. They do not include unearned income which the person did nothing to earn, such as interest on a savings account at a bank. An income is typically seen as a regular amount that you can rely on. Earnings are whatever sb manages to earn and may vary from month to month or year to year.