What is the ruling regarding feeding your pet (cat) with sacrificial meat. What about stray dogs?
The basic of a sacrifice is that the offered sacrifice animal is halal and has been sacrificed (slaughtered) in a halal manner.
It is certainly better if you feed it to people (for details see for example What is the basis for giving meat of qurbani as a gift to relatives and friends?), but it doesn't harm if animals ate from it once the sheep or cow or camel you have sacrificed was slaughtered. See also this fatwas on islamweb #130037 and #183747 both in Arabic language.
The prophet () said in a long hadith:
And we have a lots of ahadith saying that it is a good deed to be kind and feed animals:
"A woman entered the (Hell) Fire because of a cat which she had tied, neither giving it food nor setting it free to eat from the vermin of the earth. "
(See in Sahih al-Bukhari, while imam Muslim reported longer versions of this see for example here)
There was a dog moving around a well whom thirst would have killed. Suddenly a prostitute from the prostitutes of Bani Isra'il happened to see it and she drew water in her shoe and made it drink, and she was pardoned because of this.
(See in Sahih al-Bukhari and Sahih Muslim)
"The merciful are shown mercy by Ar-Rahman. Be merciful on the earth, and you will be shown mercy from Who is above the heavens. The womb is named after Ar-Rahman, so whoever connects it, Allah connects him, and whoever severs it, Allah severs him."
(See for example in Jami' at-Tirmidhi)