He does not have any work; can he stay with his paternal aunt who is married to a Christian?

Firstly: 

We ask Allaah to make things easier for you, and to relieve your distress and grant you provision from His bounty. 

Secondly: 

If what you mean by adoption is that you are named after the person who adopted you and you are regarded as his son with regard to mahrams, inheritance etc, then this is the kind of adoption that is haraam and was abolished by Islam. 

But if what you mean is that he took care of you, sponsored you and treated you kindly, without your taking his name, then there is nothing wrong with that, rather it is praiseworthy and it is hoped that the one who does that will be rewarded. See question no. (10010). 

It is obvious that according to shar’i rules, you are a “stranger” (non-mahram) in this house, so you cannot be alone with the sister of the one who adopted you, or with his wife or daughter, and you are not entitled to inherit from any of them, and your wife cannot uncover in front of the one who adopted you, and he cannot be alone with her, because he is not your father according to sharee’ah. 

Thirdly: 

It is not permissible for a Muslim woman to marry a kaafir, whether he is a Jew, a Christian or anything else, because Allaah says (interpretation of the meaning): 

“And give not (your daughters) in marriage to Al‑Mushrikoon (polytheists) till they believe (in Allaah Alone) and verily, a believing slave is better than a (free) Mushrik (idolater), even though he pleases you. Those (Al-Mushrikoon) invite you to the Fire, but Allaah invites (you) to Paradise and forgiveness by His Leave, and makes His Ayaat (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to mankind that they may remember”

[al-Baqarah 2:221] 

“then if you ascertain that they are true believers send them not back to the disbelievers. They are not lawful (wives) for the disbelievers nor are the disbelievers lawful (husbands) for them”

[al-Mumtahanah 60:10]

Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him) said: The Muslims are unanimously agreed that a kaafir cannot inherit from a Muslim and a kaafir man cannot marry a Muslim woman. End quote from al-Fataawa al-Kubra (3/130). 

What the sister of your adoptive father has done by marrying a Christian man is a great wrong, and it is an invalid marriage which must be annulled; it is not permissible for her to stay with this man under any circumstances. She also has to repent to Allaah and beseech Him to forgive her and pardon her. 

It is not permissible for you to live with her in the presence of the husband mentioned, because that involves remaining silent about this great wrong, as well as what you have mentioned about him drinking alcohol. 

All of this is in addition to the fact that this woman is not really your paternal aunt, so it is not permissible for you to enter upon her or be alone with her, let alone live with her in the same house! 

Fourthly: 

You should look for permissible work by means of which you can take care of yourself and your family. Be sure that provision comes from Allaah and that there are many means of acquiring provision, although some people are unaware of that. The Prophet (peace and blessings of Allaah be upon him) said: “By Allaah, for one of you to go out and carry firewood on his back and sell it is better for him than to ask a man who may give him (something) or withhold from him.” Narrated by al-Bukhaari (1470) and Muslim (1042). 

You have an example in ‘Abd al-Rahmaan ibn ‘Awf (may Allaah be pleased with him). Al-Bukhaari (2048) narrated that ‘Abd al-Rahmaan ibn ‘Awf (may Allaah be pleased with him) said: When we came to Madeenah, the Messenger of Allaah (peace and blessings of Allaah be upon him) established brotherhood between me and Sa’d ibn al-Rabee’. Sa’d ibn al-Rabee’ said: I am the wealthiest of the Ansaar, and I will give you half of my wealth. And see which of my two wives you want; I will give her up for  you and when she becomes permissible (after the divorce and ‘iddah), you can marry her. 

‘Abd al-Rahmaan said to him: I have no need of that. Is there any market in which trading is done? 

He said: The market of Qaynuqa’. 

The next morning, ‘Abd al-Rahmaan went there and brought some dried yoghurt and ghee, then he went there the next day, and soon ‘Abd al-Rahmaan came with traces of yellow perfume on him. 

The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Have you got married?” He said: Yes. He said: “To whom?” He said: To an Ansaari woman. He said: “How much (dowry) did you give her?” He said: The weight of a date stone in gold (or a date stone of gold). The Prophet ( (peace and blessings of Allaah be upon him) said: “Give a wedding feast, even if it is with just one sheep.” 

So seek the help of Allaah, and do not feel helpless; ask Allaah to make you independent of means by His bounty. 

And Allaah knows best.