Should he offer the udhiyah or pay off the debts that he owes?

Praise
be to Allah

Paying off debt takes precedence and is more important
than offering the udhiyah during the days of Eid, for a number of
reasons: 

1.

Paying off debt is obligatory, whereas offering the udhiyah
is a confirmed Sunnah. What is Sunnah does not take precedence over what is
obligatory. Even according to the view of those scholars who say that the
udhiyah is obligatory, paying off debts takes precedence over it, because
the udhiyah is only obligatory – according to those who say that it is
obligatory – for the one who is able to afford it, and the one who is in
debt is not able to afford it. 

2.

Paying off debt discharges one’s obligations, and offering an
udhiyah will lead to one remaining under obligation, and undoubtedly
discharging one’s obligations takes precedence over remaining under
obligation. 

3.

Paying off debt is a duty that is owed to other people,
whereas offering the udhiyah is something that is recommended to be done for
Allah, may He be exalted, and the dues owed to people take precedence in
this case. 

4.

Moreover, leaving the debt exposes one to grave danger,
because there is the fear that the debtor would have to pay off his debt on
the Day of Resurrection from his hasanaat (good deeds), if Allah does not
pay it off on his behalf. That is a matter of grave danger, because on that
Day the Muslim will be in the greatest need of every single hasanah. 

Thus it becomes clear that paying off debt is more important
than offering the udhiyah, and no exception is made from that except in the
case where the debt is deferred for a lengthy period, in such a way that the
debtor thinks it most likely that he will be able to pay off the debt when
that time comes, if he offers the udhiyah now, or he has given some
collateral for his debt that will make it possible to pay it off if he is
unable to do so when the time comes. In that case it is permissible for him
to offer whatever udhiyah Allah enables him to, and he will have the reward
for that with Allah, may He be exalted. 

It says in al-Liqa’ ash-Shahri (no. 53; question no.
24):

Question: What is the ruling on offering the udhiyah if a
person owes a debt to be repaid in the future? Is it acceptable, or must he
seek permission from the one to whom he owes the debt? 

Answer: 

I do not think that a person should offer the udhiyah when he
owes a debt, unless the debt is to be paid in the future, and he knows in
his heart that when the time for repaying the debt comes, he will be able to
pay it off. In that case there is nothing wrong with him offering the
udhiyah; otherwise he should save the money that he has in order to pay off
the debt. Debt is a serious matter, my brothers. If a man (who had died) was
brought to the Messenger (blessings and peace of Allah be upon him) for him
to offer the funeral prayer for him, he would refrain from offering the
funeral prayer for him. Then one day one of the Ansaar (who had died) was
brought to him, and he took a few steps, then he said:

“Did he owe a debt?” They said: Yes. He said: “Offer the
funeral prayer for your companion.” And he did not offer the funeral prayer
for him until Abu Qataadah (may Allah be pleased with him) stood up and
said: I will pay the two dinars (that he owed). He said: “Are you paying
these two dinars to the creditor to absolve the deceased of his debt?” He
said: Yes, O Messenger of Allah. So he came forward and offered the prayer.

When he was asked about martyrdom for the sake of Allah and
whether it would expiate everything, he said:

“Except debt.” Martyrdom does not expiate debt, so it is not
an insignificant matter. So save yourselves and do not let the country be
struck by financial calamity in the future, because those who take on debts
and take the matter lightly will go bankrupt later on, then after them those
who lent them money will also become bankrupt. The matter is extremely
serious. Allah, may He be glorified and exalted, has stipulated that
financial duties (as prescribed in Islam) are not obligatory unless a person
can afford to do them, so one should praise and thank  Allah for that. End
quote. 

It says in ash-Sharh al-Mumti‘ (8/455): 

If he owes a debt then he should start by paying it off
before offering the udhiyah. End quote. 

See also the answer to question no. 41696 

And Allah knows best.