I'm 63. I made withdrawals from a 401k without having tax withheld. When do I owe the tax? Immediately, quarterly, or end of year tax filing?

[xmasbaby0]

In January/early February you will receive a 1099R from the custodian of the account.  You will enter the information from that 1099R on your 2019 tax return.  It will be added to your taxable income and you will be taxed according to your tax bracket.  If you expect to owe over $1000 at tax time, you might want to make an estimated tax payment by going to the IRS site.  You have not mentioned whether you are also collecting Social Security.  Your SS might be taxable, depending on how much income you have altogether in 2019.

https://www.irs.gov/payments

[Hal_Al]

Simple answer: Immediately. You file for 1040-ES (estimated tax payments) to do so or pay at this IRS site (be sure to select 1040ES):

https://www.irs.gov/Payments

But taxes aren't simple. 

You should pay in quarterly estimated taxes if you don't have enough withholding taken out to cover the tax on all your income. 
You should make estimated tax payments for the current tax year if both of the following apply:
- 1. You expect to owe at least $1,000 in tax for the current tax year, after subtracting your withholding and credits. 
- 2. You expect your withholding and credits to be less than the smaller of: 90% of the tax to be shown on your current year’s tax return, or  100% of the tax shown on your prior year’s tax return. (Your prior year tax return must cover all 12 months.)

You would normally make 4 equal quarterly payments. But, since you did not already make 1st & 2nd quarter payments, your 3rd quarter payment should be large enough to cover the tax attributable to the 401k distribution.