Reading a file ON the device is offline. If you can turn off WiFi/3G and read, then it's never an "online" reading. There are loads of Android applications. I've tried dozens. I use Lithium for epub (I convert anything not epub and not a PDF to epub) and use Kodi for PDFs, but PDFs need a 10" screen minimum typically.
Reading actually Online without any downloading (i.e. WiFi, Broadband or Mobile connection must be active) uses a browser. Always.
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