I have a small LLC of which I am the sole owner and employee, have an EIN.
Assuming you have never filed IRS Form 2553 to be "treated like an S-Corp" or form 8832 to be "treated like a C-Corp" for tax purposes only, then under no circumstances and with no exceptions can the owner of a multi-member LLC or single member LLC be an employee of that business. You can not and will not issue yourself a W-2, 1099-MISC or any other type of tax reporting document. There are no exceptions.
When I receive a 1099 for part time income for this LLC do I file with my personal taxes of have to file separately as a business?
Since a single member LLC is considered a disregarded entity by the IRS, all business income and expenses are reported on SCH C as a physical part of your personal 1040 tax return. It doesn't matter if you're filing a joint return either. If you have no employees, then it doesn't matter if you use your EIN or your SSN on your SCH C. Most likely if you receive any 1099-MISC's they will have your EIN on them. So it makes things simpler if you use the EIN on your SCH C so that things match up. One note of importance here.
Since your EIN is tied directly to your SSN, it *does* *not* *matter* which is on any 1099-MISCs you may receive and it *does* *not* *matter* if you use the EIN or SSN on the SCH C.
However, if your single member LLC has employees, then you are *required* to use the EIN on the SCH C.
In all cases, you will still use your SSN on the main 1040 tax return no matter what.
