Your capital losses will offset ordinary income and decrease your total income.
However, if you are self-employed, you have 2 different types of taxes on that income. One is the regular ordinary tax and the other is Self-Employment taxes which is 15.3% of your net self-employment income. Your self-employment taxes are only reduced by your business expenses and other business related items, not by things like itemized deductions or your standard deduction.
So, if you have $20,000 in self-employment income after expenses, you will have $3,060 in self-employment taxes. This is calculated separate from your ordinary income. If the $20,000 is your only income, then you would have the $3,000 subtracted from then, then you would have your standard deduction deducted from that so if you were head of household, you would have no taxable income, but you would still owe $3,060 for your SE tax because that is the Medicare and Social Security taxes. Various credits would also affect your ordinary taxes but not your SE taxes (Unless they are refundable, then that amount will be used to pay for your SE tax instead of being sent to you)
In this situation, you would not see any benefit from your loss carryovers because it will only reduce your taxable income, not your self-employment FICA taxable amount.
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