Linux machines do not function correctly without swap. This is especially
true with 2.6 kernels... swap can be 1 byte but it has to exist :-) As
you are seeing, the OOM killer will go on a rampage (pun not intended)
without any swap. The OOM killer can be disabled, but I don't recommend
it.
Swap should be 2x physical ram. But one can get away with less.
--Ricky