The majority say qurbani / udhiyah sacrifice is an “emphatically recommended” action following the Prophet’s way, on him be peace — and notably this was also the opinion of Abu Bakr and Umar, Allah be pleased with them, the first two Rightly Guided Caliphs after the passing of the Prophet, on him be peace.
A noteworthy minority (including the Hanafi scholars) say qurbani (udhiyah) sacrifice is an obligation (wajib). (For a detailed explanation see What Is the Qurbani Sacrifice?)
Is it one qurbani per household or per person?
Scholars of the majority opinion — the ones who say the qurbani / udhiyah sacrifice is an emphatically recommend Sunnah — tend to also say that one sacrifice share (meaning a sheep or goat) suffices for an entire household that can afford to sacrifice, whether that household is headed by an eligible man or a woman; and they define a household as whoever lives together with one another as a family with shared finances (not just parents and children, in other words).
An even smaller group of scholars who share the opinion that the qurbani / udhiyah sacrifice is an obligation (wajib) rule that this obligation rests upon each individual Muslim (fard ‘ayn) who has the surplus means, sound mind, and is of age — whether male or female. This means each eligible person must account for a sacrifice share (either a goat or a sheep, or be one of seven intended to share in the sacrifice of a cow or camel).
How strong is the Sunnah of qurbani?
Very.
First, let’s say that there is a profoundly ignorant idea that is rampant among Muslims — because of our lack of education in our religion and our deficient spiritual development — that something being “Sunnah” means you don’t have to do it. The Sunnah — way, actions, and approvals of the Prophet, on him be peace — is there precisely for us to follow and do likewise. To turn away from the Sunnah is very high-risk.
Allah told Prophet Muhammad, on him be peace:
Say to the believers: If you love God, then follow me. God will love you and forgive you your sins. For God is all-forgiving, mercy-giving. Say to them: Obey God and the Messenger. And if they turn away, then know that God does not love the disbelievers” (Surat Aal ‘Imran, 3:31-32).
So, to have the means and not offer sacrifice at the proper time of Eid al-Adha (after the communal prayer!) is reprehensible (makruh). That is, it is hateful not to offer sacrifice if you have the wealth to do it on the 10th, 11th, 12th, and 13th of Dhu’l-Ḥijjah.
If Allah has given you the wealth to do the qurbani / udhiyah sacrifice, it is far safer and better for you to do it, regardless of whether it is an obligation or a confirmed practice of the Prophet, on him be peace. Whoever has the means should offer sacrifice in the days of Adha. This safeguards your worship, ensures your proper reverence for Allah, and demonstrates that you are in willing submission to Allah. Otherwise, you risk becoming blameworthy.
What to do with the qurbani / udhiyahmeat?
Eat from it (preferably the first thing you eat that first Eid al-Adha day) and keep a third of it for your household to eat from.
Distribute a third of it in charity to the needy.
Gift a third to loved ones, neighbors, and friends.
Can you give from your qurbani to non-Muslims?
Yes, especially to the poor, relatives, and neighbors.
(For a comprehensive look at qurbani,udhiyah, and Eid al-Adha see What Is the Udhiyah / Qurbani Sacrifice?)