Hey, I don`t have any specific suggestions on hostels, but be sure to check out HostelWorld.com. Remember that location is EXTREMELY important because it will save you a lot of time and money from inter city transportation (Now that I remember, I stayed in Durty Nellys hostel in Amsterdam and it was good!! They have breakfast which will sure save you a meal each day).
I don`t know if you have your transportation tickets already bought but check out skyscanner.net. That site will list you all the low cost airlines. From there, you can go to the airlines sites, but it is a great site to compare prices.
Since you have very little time, I suggest you see the musts (which is where all the tourists go).
London musts: Picadilly, British Museum, Guard´s change, Tower of London (be sure to get the free tour inside. It´s great!!!), Parliament (you can even go inside), War Museum (if you`re interested in the Holocaust history)... if you like theater, try to go to a play at night. They are amazing!!!
Amsterdam musts: Van Gogh museum, Anna Frank house, Take the free tour that meets at 10 a.m. and 2 p.m. (I think) at the obelisque (you just tip the guide at the end. It is great!!)... And there is a possibility that the red light district is closing!! So be sure to visit the strip clubs (I am not a pervert. From what I know it is a good show and about 40% of visitors are women!!! It costs around 25Euros). I missed it which I truly regret.
Paris musts: Eiffel Tower (be sure to go early because the queu can be looooong, Louvre museum, Orsay Museum, Champs Elisee, Arc du Triumph, Notre Dame, Sacre Coeur... How many days will you stay?? Be sure to ask for the week ticket for bus and trains. Even though you may not stay there for a week, it will save a LOT of money.
Berlin musts: Checkpoint charlie (visit the museum also), the remaining berlin wall, Pergamon Museum, Brandenburg gate... It`s been a while since I went there...
Well, hope this helps. If you have any more questions, feel free to ask.
Have a great trip!!!