Typically, users cannot directly convert their .edrw files (SolidWorks eDrawing) to other formats, because eDrawings are exported as a publishing format that is not meant for further editing, just viewing.
The question whenever a conversion of .edrw files is possible largely depends on how the file was exported, i.e. users may 'lock' the files during the export procedure. It should be possible to open unlocked files in SolidWorks (with eDrawing plugin of sorts) and recover the designs. For locked files, there appears to be no way to access the source.
In these cases, the best course of action would be to obtain the original SolidWorks source (most likely .slddrw file), which can be potentially exported to DXF or any other suitable format with dedicated CAD converters (see slddrw to dxf conversion).
However, it is likely that to handle these files, you will need access to SolidWorks and third party apps won't help you much.
Updated: November 4, 2016