Train Group Tickets

I didn't find any reference to the group tickets in the English version, only the German one. Probably because these tickets apparently cannot be bought online, only per phone or at the DB centre in the train stations in Germany.
Here's the link to the German page, the phone number is at the end:
http://www.bahn.de/p/view/preise/gruppen/gruppenpreise.shtml

Depending on where you travel, the Ländertickets or Happy Weekend ticket can also be a good deal. They are for five people, but even when you need to buy two of them it will be cheaper than getting six singles.

Are there any children in your group? On long distance trains children under 15 are free, provided their names are mentioned on their parents' tickets.

A brief summary to the Bahn.de-page on group-travel amsel has kindly linked to: Groups get a discount as long as they book ahead (the earlier the better, i.e. more discount), groups commit themselves to a selected train, number of seats available to groups are limited. You cannot book online, you'll either have to call them (phone-number: see link by amsel) or buy at the station.

The discount will be 70% if tickets are booked two weeks in advance to 60 % (one week in advance) to 50% (one hour in advance) - so a stretch like Cologne-Berlin would be 102 Euro full-fare/person, 51 Euro group-fare (50%)/person, 30 Euro group-fare (70%)/person.

The Länder-Tickets+ and +Happy-Weekend-Ticket as mentioned by amsel are useless to you, as your itinerary is far too ambitious to be tackled by (slower) regional and local trains...

To nautiker, my itinerary now has changed and it is not as rushed as before. Appreciate you linking your answer with reference to my earlier itinerary.

To all: So can i conclude that the only way to book the tickets more than 14 days in advance is to call them up? Are the 70% discounts guaranteed?

Yep, the 70 % discounts are guaranteed. The people at the call center are very knowledgeable, they might be able to find you even cheaper deals by giving you seats on a different train than the one you originally picked. Note that seats with the cheaper 70 % discount fare can sell out for a certain train. In this case you'll either have to take another train (usually not a problem, the call center agent will automatically book you on the train running an hour earlier or an hour later) or pay a slightly higher fare. Best call them and book as early as possible.