I've only done a little bit of Android development with VIM, but I'd very much suggest getting your head around Ant (which the SDK uses to build projects from the command line), and perhaps Maven if you're daring. You'll be using Ant a lot!
There are a few tab/auto-complete VIM scripts around, but don't expect them to be anywhere near as quick or useful as Eclipse. I've found myself doing a lot more typing than I'm used to from Eclipse...
To build and reinstall your modified app to the emulator, simply run ant reinstall from the project root. Map this command in Vim to your key combination of choice.
I've used typical Vim setup: NERDTree, FuzzyFinder, and omnicomplete. Java syntax highlighting works out of the box.
Never bothered to install Eclim, omnicomplete works just fine in most cases.
Both of what @Dave and @buru suggested led me to work on a plugin for Vim that'd help you work on development in Vim for Android applications. Feature parity to top-level tools like the visual development isn't there yet, but I was wondering if we could generate some components by using Fries and extending it.
The plugin is called android.vim and it was on Github @ jalcine.github.io/android.vim. I'm very open to ideas and pull-requests so feel free!
Edit: I've taken down this plugin because I haven't the time or focus to work on it :(
I have been working on a vim plugin for android development: https://github.com/hsanson/vim-android. Still work in progress but it has most functionality needed for android development using vim.
I still have some issues to solve but most are not related to the plugin:
Gradle errors from aapt report the wrong file. This makes jumping to the error
from the quickfix window a pain as it opens the wrong file.
I cannot make javacomplete work correctly. When auto completing a class I wrote
it gets stuck in "Searching..." and when auto completing a library or external JAR
method javacomplete spits hundreds of errors making it impossible to use.