Customer files containing strokes can be used as is in Omega, or you can turn the strokes off in Omega or you can convert the strokes to vectors.
On the gaps where colors touch colors, this is caused by the knocking out of underlying layers unless the path is set to "overlap" or "overprint". There are a number of approaches. If you are printing from vectors, the first choice is to use the Choke and Spread features of Omega. This creates an outline of the top color and sets it to "Overlap" the underlying color. This works well in simpler layouts but will not work as well in complex layouts with numerous colors touching other colors. You get into issues of conflicting orders of colors to be printed.
The work around on complex jobs is to either manually manipulate the vectors to overlap and set the overprint instructions accordingly along with setting the color print order in the 1234 dialog
or
convert all your spot colors to process colors and print as CMYK. This is the easiest and most effective solution IMHO for designs with more than two colors touching. The gaps are eliminated because CMYK works on percentages of the four process colors and will blend together nicely in most cases where colors touch colors.
If you convert to CMYK, you must do so with each spot color individually. I then recommend that you become familiar with the different choices for halftone dot patterns and the effect of LPI settings with them. If you want to emulate the look of a spot color, you will want to look at Classical Dot as your halftone type and a setting of 70.7 for the LPI. When you output the job, it will be subject to color management profiles. I recommend that you turn off the automatic management and manually select the profile named "Gerber Edge II 300 DPI CMYK". You do this in the 123 dialog of GSPPlot. That particular profile is an excellent generic profile that will provide you with very acceptable results in the majority of printing situations.