You could try some Watco medium walnut danish oil. You want be very careful with a stain unless you lightly sand and prep the surface. Reason is that since it s "oiled", as likely as not the oil is no longer "even" and an application of stain may darken the veneer unevenly.
I would recommend that you wipe the speakers down with some "laquer thinner", changing cloth between each panel. Then wipe them down several times with mineral spirits. This generally will "lift" virtually most of the old oil out.
You can use a random orbital sander with a 600 grit pad (you will need 8 pads total), and very lightly sand (more of a polishing...) each panel. You can do it by hand, but the results will not be as even and it will take a considerable length of time. Using a random ordbiatl is not difficult, and if you have no experience, you can experiment with some scrap plywood, etc. The key is to break, or expose the surface of the wood to allow for the lifting of the residual oil.
Wipe them down with a mineral spirits damp cloth to remove any residue. Keep wiping them in this fashion until the cloth is clean and no (or very little) residue comes off. You will need a pack of cotton shop towels for that. At that point, you can more safely experiment with some stain. You should find that the panels are now a more consistent hue.
I recommend Minwax "Special Walnut", as it is similar to what a vintage factory hue will appear like now. The factory did not "stain" them, but applied a BLO based oil which naturally darkens over time.
Mix it about 50/50 with mineral spirits to start with. Wear gloves (which you should wear when handling any oils or stains..), and using a rolled up 6" wide (about 12" long) piece of cotton cloth, wipe the mixture on, let sit for about two minutes, and wipe any excess off. Check your results. Do it again, etc. until you achieve the hue desired. After the staining, let them dry for at least 24 hours. Then apply the Watco danish, BLO, etc. When I stain first, I use a non tinted Watco, or Watco Danish Teak which is very, very light.
Look at: http://forums.klipsch.com/forums/t/117315.aspx
Hope that is of some assistance.