You will need to convert from 3d cartesian coordinates to polar coordinates. This should not be difficult but you need to specify a frame of reference.
Suppose we specify the following:
* positive x axis is equivalent to RA 0, Dec 0
* positive y axis is equivalent to RA 6 (RA 90 degrees), Dec 0
* positive z axis is equivalent to Dec +90
* assume one light year is equal to the distance light travels in a Julian year (365.25*86400*299792458 = 9,460,730,472,580,800 metres). (NOTE: Celestia's light year may have a slightly different length but as long as the distance is roughly right and all distances are divided by the same value then the results will come out okay.)
Then it should be possible to apply some trigonometry or vectors to convert the co-ordinates. It's been more than twenty years since I did this kind of maths so it may be necessary for you to do some research online.
But I do know that the distance is equal to the square root of (x^2 + y^2 + z^2). Divide this by 9,460,730,472,580,800 to get a distance in light years.
My familiarity with Eve Online makes me think that you will eventually want to link these star systems with lines to represent the jump routes. Ways of doing this are discussed in this topic:
Lines between stars or fictional planet systems.