These terms are in no particular order, just as they come to mind.
The female sheep is called a ewe and the male a ram. The female goats are does and the males, bucks. The female lambs are ewe lambs and the boys are ram lambs, and the male baby boy goats are bucklings and the females doelings. But, I have heard any referred to as anything else and sometimes have to decode what is actually meant. People often say ram for a male goat. They refer to the female as a nanny and the buck as a billy, which is hillbilly talk for the goats, though even I got that.
When a female is in gestation, the farmers say all sorts of funny things. They refer to the udder as the "bag" and when the udder is filling prior to birth, the term they use is "baggin' up". Up is used a lot actually, not sure why. When the male goat or sheep is breeding, it is sometimes referred to as 'marking' which may come from the actual marking harness worn in some flocks and herds, a contraption with a coloured crayon that leaves colour on the ewes that were bred. I dunno about that one either.
Chewing can either be up or down and sorting is always out. Lambing is always out, as in lambing out or lamb out. Heading is out or in.
Castrating is banding, or ringing. A ram's testicles are the 'sack'.
A ewe ready to give birth is put in a jug, which is a small compartment or stall, and the aim is to give her privacy to bond with her lamb(s). I don't know how they did it without the farmers all these centuries.
When giving instructions, they always give ownership. An example, is, " Take your lamb bucket and mix your replacer with your water." Never mind trying to figure out why, but that is how it is.
When a lamb is retained for breeding, it is referred to as kept back.
Flushing refers to feeding ewes richly, hoping they will produce more eggs and fertilization will occur, thereby producing multiples.
The country expression is 'waiting on', not waiting for, as city folk would say.
I am sure there are many more expressions that I have not included here, but I am slowly learning this new language. I am not likely every to adopt it, however; I do know now what is being referred to, so have made pretty significant progress.
Oh, and the penis of an animal is a pizzle!