Answer: Here is a site showing a photo of a night blooming cereus (Epiphyllum oxypetalum) http://www.epiuniverse.com/NightBloom.htm which is related to the Christmas cactus and in fact looks a bit like it, with floppy flat straggly branches and sounds a bit like yours. A more upright columnar type of cactus is also sometimes called night blooming cereus and this is the Cereus peruvianus. It also blooms at night and could be what you saw in Florida.
Most cactus are cyclical bloomers and need to have fairly bright light in order to bloom. Some also need a cool (50 degrees) dry or nearly dry spell to simulate a mild winter. Some also appreciate simulation of shorter days during that cool spell, say from October to December. After that, bringing them into a bright slightly warmer location and a resumption of watering should induce blooming. Most of them do bloom on new growth, however, so you might want to leave some of those odd shoots intact and see if that's where the flower buds form on your plant. Finally, you might try using a fertilizer intended specifically for cactus or (easier to find) tomatoes on your plant being careful to apply it only to the roots and not to the above ground portions of the plant.
Finally, in my experience, the taller columnar types tended to bloom once a year during the summer -- they resented wintering indoors and waited until they were outside on the porch again to bloom.
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