I am not sure of literal meaning of "Aila". Neither am sure of it belongs to which language, though Hindi film song --"Aila re ..." or Sachin's Pepsi's ad suggests that "Aila" may be a slang, at least . Aila's femininity or masculinity is something I am leaving up-to linguists or ... the hard nosed people who debated and debated with me on it ;).
But gone by the essence in which this term was used in Songs or Ads, "Aila" carries a sudden surprise element though the imposition of surprise is not forceful. So though it is delivery of surprise ... its not something which will make you run bizarre. "Aila" has soft intensity.
"Aila" has killed hundreds of people this time. Its cyclone Aila. Aila is just a noun here, its verbal context described in upper stanza has no connection.
Actually in the consciousness of Indian mindset, Cyclone "Aila" or floods or earthquakes or any other cacophony are verbally "Aila". Surprising, soft intense.
Aila's are forgotten ... till next Aila comes and passes away ...