In general, your filing requirement is based on your amount of taxable income. While VA disability is generally tax free (see the following link here: https://benefits.va.gov/BENEFITS/factsheets/serviceconnected/Compensation.pdf), and social security is also tax-free if there is no other source of taxable income, you may still want to file a final tax return. This would provide the social security administration and IRS with final notice of his death (the social security administration should know already, as they have stopped his social security payments).
The more difficult task may be to electronically file a return with no taxable income, as TurboTax will not e-file a return with no taxable income (you can always file by mail). To get around this limitation, you can put $1 of income from a bank account as investment income, which will allow the return to be e-filed. You can find this in the "Wages and Income" section under "Investment income."
And the home should pass to you tax free - the capital gains on the home are erased at death (this is called the "step up" in basis). It is not reported on a final income tax return unless he sold it before he died. For you, as the inheritor of the house, you may have a capital loss on the property sale, if you incurred expenses to sell it (broker fees, closing costs, etc.) and you did not live there (i.e. - use the property as a personal use asset). It would be reported as a capital loss on your tax return.
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