Well, you can definitely knit a round object using straight needles. You would need to knit the project flat and then seam it to make a round shape. I would recommend using a 'mattress stitch' for creating your seam. Imo it produces the cleanest seam.
If you were to knit the object in the round, there are a number of different techniques and types of needles you can use to accomplish this. When I first began knitting hats in the round, I used a 16" circular needle, and when the circle became to small to accommodate the circular needle, I switched to double pointed needles.
I have used the 'Magic Loop'method for small diameter circular knitting for years; the technique usually requires a minimum of 30" length circular needle. There is no need to change to double pointed needles when using this technique.
Recently I have begun to use two circular needles to knit certain round projects. I have not knitted enough projects using this method to know how I feel about this technique, but I certainly do like it and may very well end up preferring it to the 'Magic Loop'.