Welcome Sliginion!
All of us here truly wish to help you get on the right track and make great soap, but I second everyone's concern that it would be in your best interest to take some time out to do more research before attempting any more batches.....
If I understand correctly, for your first batch that came out feeling greasy, you used 3 lbs lard and 3.5 wood ash....
Can you tell us more about how you went about preparing the wood ashes? Do you know what the strength of it was? If you used a particular recipe online, can you point us to it? It will be of great help to us in attempting to help you if we know all the specifics. As DeeAnna said, it's a very tricky process making soap using wood ashes. For what its worth, I've been making soap 10 years and I have no desire to even think about trying to attempt making soap from wood ashes.
And for your second batch, you used 16 oz lard, 12 oz goats milk, and 3.3 oz lye water made with crystal lye. ....
Can you tell us more about your second recipe such as where you got it or how you came up with it, and also how you went about making your lye water out of the crystal lye? From you description above, it sounds like your total lye solution weighed 3.5 oz, but we'll need to know the actual weight of the lye you used in proportion to the weight of your water. Also- just to be sure- was the crystal lye you used 100% NaOH?
IrishLass