Since you have referred twice to Sony Vegas, you must have an old version of Vegas Pro because the last version of Vegas Pro from Sony was version 13 which was released some 7 years ago. See https://www.vegascreativesoftware.info/us/forum/sony-vegas-vs-vegas--119881/ for further information.

As you will see from File/Export in Vegas Pro, there is no specific export project file for Edius but there is the EDL text file export option. While there may be someone on this forum who may know whether or not EDLs can be imported into Edius, you should also look at Edius' user manual re its import capabilities.

As has been mentioned in other forum posts re exporting from Vegas Pro to other NLEs, the success of export/import is a rather mixed bag and the best that can usually be expected is that just the very basic edit will successfully open in the other NLE. FX, color grading and so on will not likely transfer especially if they are Vegas Pro proprietary FX.