Will I be elegible for the 144HRS visa?

No, your journey is not eligible for any kind of visa free transit scheme. You need a visa obtained in advance.

As far as you know, to be eligible for 144 hour visa free transit you cannot have more than one stop within mainland China and your itinerary has three stops. Just to simplify, I would suggest you to look after a following itinerary if you want to enjoy 144 hour visa free transit in Beijing:

Hong Kong - Beijing - Hanoi

This is one example and you can use some different if you want, but have in mind the requirement that just one stop is allowed within mainland China. If you make just one additional of any kind, this disqualifies you for 144 visa free transit scheme.