I have really good luck getting out oily stains with Dawn dishwashing liquid. I just rub it in, let it set until next washing or go ahead and wash immediately. I have also heard that peroxide with Dawn does a wonderful job. I think line drying on a very sunny day helps also! Pineterest has alot of wonderful ideas on how to get out stains. Good Luck! And a very merry Christmas to you, also! :-)

The musty smell can probably be removed with washing.

Bleach is pretty tough on fabric. The older the fabric, the more chance that bleaching can hurt the fabric. Try to avoid using chlorine bleach on delicate fabrics.

There are special cleaners out there for vintage fabrics. But mostly, I use either OxyClean or Clorox 2--both have no chlorine bleach in them. That's for general stains. And Dawn for oily stains.

What I do is soak the item in a dishpan full of warm water and either OxyClean or Dawn. It frequently takes several soakings to completely remove a stain. So I'll start soaking in the morning and change out the water in the evening and let the item soak all night. This could go on for several days.

Unless there's delicate thread work or lace on the linens, I'd start by washing in a machine on the delicate cycle. Or handwashing with a long soak. Then line dry the linens out in the sunshine, as sun is also a good bleaching agent. But do not put the linens in the dryer, as that will only set stains.

If the linens need more help, start soaking them in OxyClean or Dawn. This would be safe even for the colored linens.

If the cross-stitch work is in color, do test the item for colorfastness first. You may have to do only cold water washes/soaks for those items. Chlorine bleach will remove the color from the stitchery, so avoid that.

I clean all of my white or off white linens with denture cleaner. Drop half a dozen tablets in a sink full of hot water and soak. It removes oil stains very well and does not hurt the material. When wet though, use care in handling by not picking them up with large amounts draping down (ball them up and gently squeeze) so as not to stress the threads if they're very delicate.