I paid 2019 taxes and have cancelled checks but IRS just sent me a letter saying I haven't paid?

Try this -

Call the IRS: 1-800-829-1040 hours 7 AM - 7 PM local time Monday-Friday
When calling the IRS do NOT choose the first option re: "Refund", or it will send you to an automated phone line.
So after first choosing your language, then do NOT choose Option 1 (refund info). Choose option 2 for "personal income tax" instead.
Then press 1 for "form, tax history, or payment".
Then press 3 "for all other questions."
Then press 2 "for all other questions."
- When it asks you to enter your SSN or EIN to access your account information, don't enter anything.
- After it asks twice, you will get another menu.

Press 2 for personal or individual tax questions.
Then press 4 for all other inquiries
It should then transfer you to an agent.
Or you can contact your local IRS office. See this IRS website for local IRS offices - http://www.irs.gov/uac/Contact-Your-Local-IRS-Office-1 or call 1-844-545-5640 to set up an appointment

How did you pay?  It should be one check with a 1040V for the total.  Did you send in the 4 1040ES slips?  Those were not for the tax due.  They were estimated prepayments for NEXT year 2020 so you don't owe too much again.  So if you sent in the wrong slips be sure to enter the estimates you paid into your 2020 return to get credit for them.