Mere oiling will probably not be enough to free up the swivel arm, it might need some help. First thing to try is heat, preferably from a hair dryer. Heat will cause the parts to expand, hopefully they will expand enough for some of the new oil to work down in where it will do some good. It might take several applications of oil and heat to get the swivel arm loose enough to move. Apply oil, heat and wait overnight.
Once the swing arm swivels the tiniest bit, you're almost home! Remove the needle, bobbin case and shuttle and hold the stitch width lever to the widest point you can get it without forcing it and bending some linkage. Run the machine at top speed, holding the stitch width lever to the right. As that new oil works its way in, you should notice the needlebar taking wider and wider strokes and the stitch width lever moving gradually to the right. When you are able to move the stitch width lever all the way to the widest stitch and the needlebar is taking full 5mm zig zags, you are done.
Ironically, the Necchi oiling diagram does not show these as oiling points and does not even direct the owner to remove the end cover to oil anything in that end of the machine. There are lots of moving parts in that location that require lubrication - the needlebar, presser bar, takeup lever, and others. Once you've taken care of the zig zag problem, before closing up the machine, put a drop of oil every place metal rubs against metal and your machine will run quieter and smoother.