I am refurbishing an old trunk. The inside is cedar but the outside is veneer. There are nicks in some spots can I repair these nicks with Elmer's wood filler?

You can, but I think it would be a mistake. The filler will darken with finish over it and with time, and just draw more attention to the trunk than the nicks do. Filler doesn't lend itself well to thin applications anyway.

If places are in danger of splintering and lifting, wipe the surface gently with thinner and apply a satin polyurethane very lightly.