Offering the udhiyah is a confirmed Sunnah (Sunnah mu’akkadah) that should be done regularly and it should be done openly and propagated among the Muslims. Some of the scholars are of the view that it is obligatory; hence to be on the safe side, it is better not to omit it except if one has an excuse. 

Slaughtering the udhiyah is preferable to giving its price in charity or donating a sheep, because by slaughtering it one draws closer to Allah, may He be exalted, and makes the ritual manifest. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

The udhiyah and ‘aqeeqah and hadiy are better than giving the price thereof in charity; if a person has wealth that he wants to use to draw close to Allah, he should offer the sacrifice himself.

Majmoo‘ al-Fataawa, 26/304 

It says in Kashshaaf al-Qinaa‘ (1/21): Slaughtering the ‘aqeeqah is preferable to giving its price in charity. The same also applies to the hadiy. This was stated clearly by Ibn al-Qayyim in Tuhfat al-Mawlood and by Ibn Nasr in his Hawaashi, because the Prophet (blessings and peace of Allah be upon him) and the caliphs offered sacrifices; if giving charity was better, they would have done that. And because of the hadeeth of ‘Aa’ishah, which is attributed to the Prophet (blessings and peace of Allah be upon him): “The son of Adam does not do any deed on the Day of Sacrifice that is more beloved to Allah than shedding blood; it (the sacrifice) will come on the Day of Resurrection with its horns and hooves and hair, and Allah appreciates the blood before it reaches the ground, so do it gladly.”

Narrated by Ibn Maajah. [Classed as da‘eef by al-Albaani in ad-Da‘eefah, 526]. And because preferring to give in charity rather than offer the sacrifice leads to forsaking the Sunnah of the Messenger of Allah (blessings and peace of Allah be upon him). End quote. 

But if your friend is aware of the need of a particular family, then he may give charity to them in particular and not to anyone else, and he may give them some charity (other than the udhiyah) and give them a larger share (of the sacrifice) and keep a smaller share for himself if he is going to spend Eid on his own and does not need his share of the udhiyah. 

If the needy family is not in the place where he is living, then he may delegate someone to offer the udhiyah on his behalf in a country or region where there are many needy people. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

If we say concerning the hadiy and udhiyah that it is mustahabb to eat one third and give one third in charity, that only applies if there is no reason to increase the portion of one of the categories of recipients. But if it so happens that there are a lot of poor people, then we regard it as preferable to give more than one third in charity; the same applies if the poor have received meat in abundance (in this case, their share may be reduced); and the same applies to what one may keep. Wherever the need is greatest, that may change the ratios given to the three categories of recipients.

Majmoo‘ al-Fataawa, 19/258 

See also question no. 36645 

If it so happens that the family that your friend is helping are in need of money and their need will not be met by giving them the meat from the sacrifice, and he does not have any other money, as you mentioned in your question, and he does not have anyone with him to whom he can give the meat or he has relatives who need this money, then he may give this money to them in charity in this case, and not offer the udhiyah this year. 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 

(Voluntary) Hajj performed in the prescribed manner is better than charity that is not obligatory. But if a person has relatives who are in need, then giving charity to them is preferable. The same applies if there are people who are in need of his spending. But if both actions are voluntary then Hajj is better, because it is an act of worship that is both physical and financial. Similarly, offering the udhiyah and ‘aqeeqah is preferable to giving their price in charity. 

Al-Fataawa al-Kubra, 5/382; al-Ikhtiyaaraat, 116 

And Allah knows best.