Thanissaro Bhikkhu seems to favor the use of the word "effluents" for asava in his translations. Even though I love his translations, I find "effluents" just as inscrutable as asava.
In a footnote in his translation of the Digha Nikaya (footnote 134, page 546), Maurice Walshe notes that asava is variously translated as 'biases', 'intoxicants', 'influxes', 'cankers', or Deadly Taints'. But he uses 'corruptions' in his text.
Of these choices, biases or intoxicants seem the most meaningful to me, though perhaps neither word fully conveys the meaning of asava.