I have 58mm filters, and I found out that the Sony filter size is 49mm. How can I use the larger filters with my Nex? Would I need a step up ring?
Would it be better to buy 49mm filters instead? Would this affect my photos differently?
Yes a 49mm - 58mm step up ring is what you need. Here is one at BHPhotoVideo for example. And here are a bunch of results at amazon. I would also consider one of the kits that come with multiple step up rings such as this: http://www.amazon.com/Fotodiox-Anodized-49-52mm-52-55mm-55-58mm/dp/B001G445Q4/ref=pd_bxgy_p_text_y
With regard to your second question about whether the step up ring would affect picture quality, the answer is that it shouldn't.
If you leave the step up ring attached then there's no effective difference between this and having the correct sized filters. The only advantage of the 49mm filters I can think of is that it would look "cleaner" (but hardly worth the extra cost).