So readiness can be increased through apps—are they only available on iPhone/iPod/iPad, or are they also available on Android? And what do I need to search to find it on the Android market? (Using an Xperia Play) If not available on Android, will I miss out on much by not using the app?
No, Mass Effect: Infiltrator and Mass Effect: Datapad are iOS only.
You're missing on a few weapons/Intel by not playing Infiltrator, and you're missing out on ways to increase Readiness from both.
This isn't really that big of a deal because it's been intentionally designed that you don't NEED readiness to get any of the achievements or endings in the game, it's just easier to get the "better" endings. Note that you can also increase readiness from Multiplayer, which also increases readiness very fast.
This app is called Mass Effect: Infiltrator. It is an iOS app so unfortunately this is a no go for androids.
All that comes from Infiltrator is the readiness, which can be increase via ME3 multiplayer anyway.
Weapons are not included in the bonuses of this app. Check out the answer to this question for more information.
This interview contains useful information on Infiltrator along with information on the android version, which is in production at this moment, this information given near the end of the interview.
There's also Mass Effect Datapad, that is supposed to have a readiness/war asset effect as well. The data pad is not available as of 11:15 AM EST 3/12/2012. It was supposed to be out the same time as Infiltrator, so I expect it to be out soon.
I have not seen any material indicating that either will be released for any platform other than iOS.