If your step dad took possession of the house because he was the beneficiary of the trust, then his basis when he received it would be the house's fair market value, which is $195,000 in your case. When he gifts it to you, your basis would be the $195,000 less accumulated depreciation that was available, whether taken or not, during the years it was rented out after your Mom died, plus any improvements made to the property and any gift tax paid when it was gifted.
When you sell the house, you report the sales proceeds less your basis and the difference is capital gain income, unless you rent the house, in which case some of the gain may be ordinary income, because of the depreciation taken. Your basis upon your sale is your original basis when you took possession of it, less depreciation available during the time it was rented, plus the cost of any improvements made.
A like-kind exchange would let you defer tax on any gain, but it is a complicated and potentially costly exercise and would entail acquiring a new rental house. Since you are related, it would be difficult to structure a sale between the two of you that would generate a tax benefit, as the purpose of it would be solely to save taxes, which isn't normally allowed.
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