As with all ant species, you need to make sure you kill the queen and immatures, which can be difficult because they are usually hidden in a nesting area.

Fire ants can easily be controlled with the use of baits.  A bait like Amdro and Amdro Firestrike (Available at many retail outlets) can be spread around the yard and the garden area.  The spinosad bait, Fertilome Coma And Get It, can be spread in garden areas.  Since "Come and Get It" is considered an all natural bait it can be used in an "organic" garden.

I would suggest going to http://fireant.tamu.edu for more information on fire ants.  Also here for information on products, http://fireant.tamu.edu/controlmethods/products/ and here http://fireant.tamu.edu/files/2013/05/2013-Fire-Ant-Bait-Misc-Control-Products-5-30-13.pdf for a printable sheet on fire ant products.

I would also suggest visiting http://www.extension.org/fire_ants, specifically here,http://www.extension.org/pages/30628/how-to-kill-fire-ants#.UodoWic_DhE for additional information.

For the black crazy ant please visit the Urban Entomology site, http://urbanentomology.tamu.edu/ants/crazy.html.

You may also want to download this older publication on Managing Household Ants:
http://www.agrilifebookstore.org/product-p/eb-6183.htm