I realize it is a bit late to discuss what you should have done. Based upon the below I am thinking the oil may just make it worse. I would ask Jim Rion for his advice on what to do at this point.
From
Strop Details and Care | Eastern Smooth
Naomi-san recommends no oiling, as this can alter the strops finish deeply. Instead, if you feel the surface of the strop is dirtied, glazed or it isn't giving the edge you want, try this:
Lay the strop face-up on a flat surface.
Get a smooth, soft cloth, like an old clean t-shirt. Do NOT use terrycloth.
Wet the cloth in luke-warm water and wring it out well--the cloth should only be damp.
Gently wipe the surface of the strop in one smooth motion. Don't scrub or press! Be careful not to get any water on the sides or back of the leather, as this can lead to hardening.
Allow the strop to dry thoroughly. If the surface still feels like it's not quite right, repeat.