What is the fastest and cheapest was of travelling the following routes?
Hanoi to Halong bay
Halong Bay to Hue
Hue to Danang
Danang to Nha Trang
Nha Trang to Da Lat
Da Lat to Ho Chi Minh City
Thanks.

Bus=cheap but slow
Plane=fast but expensive
and every body know that. Except the route of Danang to Nhatrang by bus is very slowwwwwwwwwwwwwww. and better take train.

People generally travel fom Hanoi to Halong Bay on a package tour so if you do this you will end up back in Hanoi where there are probably more options for travel south. Buses are awful, especially overnight. Travel by train if you can.
WeiLong in Vietnam

The cheapest option (apart from walking) is definitely the opentour bus. That was only $20US for many stop overs for a day or more along the way from Hanoi-Saigon or vice versa and whilst in Hanoi you can get cheap tours to Halong Bay. If you had a bit of extra time when you arrived in Saigon/Ho Chi Minh City, you could get the 3 day 2 night Mekong Delta tour to Phnom Penh/Cambodia and then see a little bit of Cambodia before getting a cheap AirAsia flight to Bangkok where you can then go where ever you need by flight.
You should check out http://www.sinhcafe.com.vn<BR><BR>DO NOT book anything through that site, just use it as a guide to see the sorts of things that are available. That is the same company that operates the opentour bus and all the cheap tours you can get in Vietnam, but the price on the website is usually a hell of a lot more than what you will pay when you purchase at one of the many tourit shops in Vietnam.

Here is the website of the original Sinhcafevn. a good, reputable company. They also have a number of tour options on their site. We did the Cu Chi tunnels and Mekong tour with them and we were very happy.
We flew from Hanoi to Hue, hired a driver from Hue to Hoi An, and then we flew from Danang to HCMC. Not the cheapest option but we were very happy with it all.