Are ESI blocking or non-blocking?
ESI with varnish is always executed in serial. They put alot of work on improving ESI with varnish 3, but still no change in that aspect. I also remember seeing some response from varnish staff saying that the feature was on their wishlist but was a tricky one to implement.
For making paralell now I guess the only option would be to implement the feature yourself.
As for Ajax vs ESI I would say the break point goes later than 5 ESI as long as they can be rendered quickly by your backend. Ajax always has the drawback of being bad SEO if used for content parts of your site.