Travel to Tokyo and Fuji Five lakes?

We are going to Japan in April from the 11th to the 23rd, flying in and out from Osaka and will be staying in Shinjuku from the 15th till the 19th, then on to Fuji Five Lakes area for one night.
Should we cancel that part of our trip because of the power blackouts, with train disruptions and the water and food shortages? Also the threat of radiation in those area's due to the nuclear power station problems.Are the problem power stations close to Tokyo? Will the treat of nuclear meltdown effect Tokyo and it's surrounding area's?

Should we cancel that part of our trip because of the power blackouts, with train disruptions and the water and food shortages?

Unless you have cancellation deadlines coming up, I don't think that you should be making the decision now. Instead, I recommend to wait for a few more days and see how the situation develops. After all, less than 100 hours have passed since the earthquake and a lot of things are still in a state of confusion, which should improve steadily from now.

Also the threat of radiation in those area's due to the nuclear power station problems.

Certainly not at the moment. It is difficult to say how it develops. I personally have not heard any expert mentioning the possibility of dangerous radiation reaching places as far away as Tokyo or even Osaka. But then again, there were a quite a few turns to the worse that the power company initially played down.

Are the problem power stations close to Tokyo?

They are more than 200 kilometers away.

Will the treat of nuclear meltdown effect Tokyo and it's surrounding area's?

See comments above. In addition to actual health concerns, there is a possibility of further confusion and stockpiling in case that the radiation threat worsens.

Please have a look at the many other threads where people are discussing the same questions as you have asked, and also the updates provided at the top of the page. Nobody here has any idea what the situation will be with trains, electricity and food supplies in Tokyo 3 weeks from now in any case- we don't know what it will be like tomorrow.

Only you can answer the question of whether or not you should go ahead with your trip.

The problem power stations are I think about 300km from Tokyo.