This animal is half goat and half sheep
When you use "is", this means that the animal in question bears some permanent traits that will either be considered a sheep or a goat based on different aspects. Maybe it's a goat-sheep offspring: it has both the genes from a goat and a sheep; or maybe one side of it is a goat, the other side is a sheep, kind of like what you'd get if you chop both a sheep and a goat in half and join each half together; etc.
Sidenote: when phrased this way, this sentence is really vague and it's very hard to pinpoint the exact meaning the speaker is getting at.
This animal is half a goat and half a sheep
When phrased this way, personally, I'd consider it to lean more to the latter meaning (one side of it is a goat, the other side is a sheep, kind of like what you'd get if you chop both a sheep and a goat in half and join each half together); but it's still quite similar to the above sentence.
This animal looks half like (a) goat and half like (a) sheep.
In this sentence, I feel like the articles can be ommitted without significant change in meaning. To me, "a" just feels like a meaningless filler without conveying much meaning in numbers.
Unfortunately, I have no other sources other than my ear.