Best way to ship a box from Hanoi to USA?

If it is worth shipping it's probably worth going FedEx or DHL.  One thing to check on either is to be sure they are quoting Economy instead of Priority.  It will increase shipping time from 3-5 days to around 7-9 but it is much cheaper. 

You can ship Vietnam Post and it is quite cheap but you aren't assured it will arrive.  I had one supplier send me something from VN to US with Vietnam Post and it never arrived.  That's my only exposure.  I'm sure others have had the opposite experience.

For me we only use FedEx but my company back home has a 70-something% disount off of list rates so it's actually pretty cheap for us.

Fedex and DHl aren't the cheapest, but they do exactly what they say they will.
It's all a matter of how much the items matter to you. If the things are nothing special, just sell them or give them away.

You can look on Facebook for a service called " Friends who deliver", maybe someone in Ha Noi is travelling back light and can bring it for you.

Thanks very much! There are some valuable items but nothing particularly noteworthy.