I know asana has an iCal feed for google calendar but I find that nearly useless without two-way syncing. Plus, Google notoriously updates the subscribed iCal feeds very infrequently—so the feed is usually out of date which actually makes it more harmful than helpful. Also, tasks show up as events; which they not.
I understand two-way syncing would have to be very limited but it would still be great if asana synced with Google tasks (or reminders). At least they could be seen as tasks and always up to date. And at least the due date could be changed or the task marked complete. It is minimal functionality but leaps and bounds ahead of an iCal feed.
Alternatively, asana could sync with events. Basically same minimal functionality as tasks, but maybe this is more feasible for asana. Downside is that tasks appear as events. Still leaps and bounds better than an iCal feed!
A completely difference approach—with vastly more functionality—is for asana to sync Google calendars on its end. So you would be able manage your Google calendars in asana along side your tasks. Judging by how many apps do this, the syncing should be relatively “easy.” I really do not know that, but “everyone” does it so it must not be big deal. I imagine the UI might be quite a bit of work though.