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It is not "illegal", per se, but there are regulations that must be followed. These regulations vary by state.
For the regulations in your state, you will need to contact the Texas Dept of Agriculture:
http://www.agr.state.tx.us/agr/program_render/0,1987,1848_5606_0_0,00.html?channelId=5606
They are used to these type of questions and should have some prepared info to send you.
Here in Wisconsin, I contacted our Dept of Agriculture, and they sent me a nice information packet that described all of the state regulations. For example, here in Wisconsin egg sales from the farm are unregulated. I can sell all the eggs I want, without grading or inspection, as long as I am selling from the premises.
If I wanted to sell to retailers or restaurants, I would need an Egg Processors Permit, need to have the necessary facilities, need to grade the eggs, and would be subject to quarterly inspection by the state.
If I wanted to sell directly to the consumer from a farmers' market or door-to-door sales route, then I would need the above, plus a Mobile Retailer's Permit.
As far as your questions about the IRS, there is not a lower limit as to the amount of income that has to be reported. If you have income you are required to report it. Your taxable income (profit) is determined by taking your gross sales and subtracting your expenses (feed, housing, electricity, water, vehicle expenses, etc.) With just a few hens you unlikely to make a profit that would be taxable.
Contact your Dept of Agriculture and see what they have to say. They will be able to give you an idea of what is permissible for a backyard producer in your state.