Take a look at Infinity Reader. It supports audio, video and all ePub3 features. The reader comes with a free book, which contains youtube video. Moreover, you can download a lot of free books.
From Android Play Store, you can use ASTRI-Bee (full version):
- Support for audio and video content within the epub ebooks, again, this is just a basic feature of epub3 ebooks, but we also extend the support of multimedia to epub2 ebooks using the adobe flash plugin(requiring that the adobe flash preinstalled on your device)
I've highlighted what concerns your question.
Ps: Appears to be a "young app"... only one revision.
Here's a couple others, but they are low-rated or in beta, so use at your own risk.
From the description in the Market, take a look @ Himawari - https://play.google.com/store/apps/details?id=jp.green_fld.himawari
Although the reviews aren't altogether too favourable.
Also, Ibis Reader has recently introduced the epub3 format into its reader - http://epub3.ibisreader.com/
Please check out Gyan ePub Reader. It is a fully compliant epub3 reader with audio and video support.
No Adobe plugins are required. It renders maths equations, SVG animations and has a read-aloud feature.
SkyEpub definitely supports epub3 (audio/video media overlay functions) See this link enter link description here