To identify each devices uniquely I would like to use the IMEI (or ESN number for CDMA devices). How to access this programmatically?
You want to call android.telephony.TelephonyManager.getDeviceId().
This will return whatever string uniquely identifies the device (IMEI on GSM, MEID for CDMA).
You'll need the following permission in your AndroidManifest.xml:
<uses-permission android:name="android.permission.READ_PHONE_STATE" />
in order to do this.
That being said, be careful about doing this. Not only will users wonder why your application is accessing their telephony stack, it might be difficult to migrate data over if the user gets a new device.
Update: As mentioned in the comments below, this is not a secure way to authenticate users, and raises privacy concerns. It is not recommended. Instead, look at the Google+ Login API if you want to implement a frictionless login system.
The Android Backup API is also available if you just want a lightweight way to persist a bundle of strings for when a user resets their phone (or buys a new device).