These questions really are too generic to give good answers to, I would suggest that you try and be a little more specific and you may get more responses.
But to try and answer them generally...
1. What are the principles that all styles of jujitsu have in common?
Basically, all jujutsu styles will have joint locks and some throws or takedowns. The general priciple is to unbalance your opponent and then apply a technique.
2. How do some of the major styles differ from one another?
Way too broad a question, essentially the differences are in the philosophy, in the application of the technique, in the types and numbers of techniques, and in the way they are taught.
3. What would you say are the major strengths and weaknesses of jujitsu?
Major strength, you have a wide range of possible responses and can scale the defence from avoidance to serious injury or death.
major weakness, takes a long time to learn properly.
4. Generally speaking how whold you rate the utility of jujitsu as a self-defense art?
Depends on the style, student and the instructor, it can be very, very good, or it can be very bad.
5. What would be some good arts one could study to compliment the shortcomings of jujitsu?
What shortcomings? I travel a lot so I studied some Karate (Ashihara & Shotokan) to supplement my punching and kicking, I also trained with a boxer to build my speed. I practise Shindo Muso Ryu for weapons work and some Arnis for close in knife fighting.
But I wouldn't recommend training in multiple styles, learn one well first, then look for something else if you feel it is required. I did nothing but jujutsu for 8 years before I was forced to look at something else when I moved away from my sensei, but I still made the effort to return regularly so that I wasn't corrupting what I knew with what I was learning.
Regards
Neil
Neil Hawkins
"The one thing that must be learnt but
cannot be taught is understanding"