If you are a resident of OK (which it appears you are from the driver's license and the domicile), you are required to file a resident return for OK even while overseas.
"Filing Requirements. Tax Year 2016. Oklahoma resident individuals are required to file an Oklahoma income tax return when they have sufficient gross income to file a Federal income tax return. "
Source: https://www.ok.gov/tax/Individuals/Income_Tax/Filing.../General_Information/
Resident...
An Oklahoma resident is a person domiciled in this state for the
entire tax year. “Domicile” is the place established as a person’s
true, fixed, and permanent home. It is the place you intend to
return to whenever you are away (as on vacation abroad, business
assignment, educational leave or military assignment). A
domicile, once established, remains until a new one is adopted.
the OK tax return (Form 511 part I) starts from the Federal Adjusted Gross Income (line 37) which is after the Foreign income exclusion is taken.
So it is very possible you may have a zero State tax liability, however you are still required to file, due to your gross income exceeding the OK filing requirement.
https://www.ok.gov/tax/documents/511Pkt-17.pdf (for 2017 tax year, however same rules apply to 2016)
Penalties are based on tax due, so if no tax is due to OK then there would be no penalty.
