The mere fact that you have no income reported on a W-2 (that is, income from employment) does not mean that you would not owe taxes. For example, a person who does not have a job, but who $5 million invested in publicly traded stock that issues dividends has taxable income by way of the dividends.
In your case, it sounds as though you are collecting rent from property which you own. The rent is probably gross income under the tax code which you would likely report on Schedule C. You will have some deductions associated with the property, such as depreciation expense, mortgage interest expense, and other things such as insurance, and other expenses which you incurred with regard to the property. If your expenses exceed the gross income, your net income may be zero or you may even have a loss, but you'll need to file a tax return nonetheless.
I do not know if unemployment is treated as taxable income. Social security ("old age pension") payments are taxable income, but social security disability income may not be income. I'm not sure about unemployment payments.
All told, whether you owe taxes or not depends on the specific facts of your situation. A lot of factors go into taxable income for the federal income tax. I recommend consulting a tax professional or at minimum, picking up a form 1040 and instructions online at www.irs.gov or in hard copy from your local library. If you meet certain conditions, you may even be able to file a tax return at little or no charge through an online provider such as "TaxACT" "TurboTax" "H&R Block online" or other provider. You may be able to find a listing of providers through the IRS website.