How do I find out if I owe the IRS money from back taxes ?

You can try this phone number for the Treasury Offset Program  to see if they show any info for you.  TOP would have data for the IRS and other participating tax agencies.

"If you have questions regarding the offset of your federal tax refund or offset of another U.S. government-issued payment, you may phone the Treasury Offset Program Call Center at 1-800-304-3107. "

https://www.treasury.gov/services/report-fwa/Pages/treasury_offset_program.aspx

If you are talking about back Federal taxes at the IRS, you can download a tax account transcript at the IRS website, but I'm not sure what all it would show in terms of arrears.

http://www.irs.gov/Individuals/Get-Transcript

Or you can phone the IRS itself to see if there is any problem with your tax account.  IRS:  800-829-1040  hours 7 AM - 7 PM local time Mon-Fri

When calling the IRS do not choose the first choice re: "Refund", or it will send you to an automated phone line.
 
First choose your language.  Listen to each menu before making the selection.
Then press 2 for "personal income tax".
Then press 1 for "form, tax history, or payment".  
Then press 4 "for all other questions."
Then press 2 "for all other questions."  It should then transfer you to an agent, but there is likely to be a long wait.

I usually use a speakerphone so I can work on something else while waiting.

Additional info added to answer above.  If you were emailed the original answer, please return to the forum to read the full info.

Do I owe the irs

You can go to the IRS web site and make an account for yourself and find all that information. If you need a copy of a past return you can also request them on your account.