What is the fate of those who heard about Islam but knew nothing about it?
What is the fate of the Christians who did only good deeds in the worldly life, and the Jews who believe in one God?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Allaah The Almighty does not punish anyone until he has already been informed beyond the excuse of ignorance, as indicated in the verse that reads (what means): {And never would We punish until We sent a messenger.} [Quran 17:15]

Informing beyond the excuse of ignorance means that Islam has already reached the person and he had the ability to know about it. Ibn Al-Qayyim explained that informing beyond the excuse of ignorance is achieved by means of sending Messengers and revealing holy Books and that man be able to have knowledge of them, whether or not he takes advantage of this ability. Anyone who is able to recognize the commands and forbiddances of Allaah The Almighty but fails to comply with them has already been informed beyond the excuse of ignorance. Consequently, such a person becomes liable to be punished by Allaah The Almighty.

It is important to note that informing beyond the excuse of ignorance differs according to various conditions, times and people. Ibn Al-Qayyim mentioned this and added that the disbelievers may be informed of the message of Allaah The Almighty at certain times and places. Certain people may not be informed of His message due to being incompetent for religious accountability such as children or the insane or due to being unable to understand the message and there are no means such as translation.

Once a person is informed of the message beyond the excuse of ignorance and he does not embrace Islam, he will be doomed eternally to Hell, as indicated in the verses that reads (what means):

{Indeed, those who disbelieve and die while they are disbelievers - upon them will be the curse of Allaah and of the angels and the people, all together, Abiding eternally therein. The punishment will not be lightened for them, nor will they be reprieved.} [Quran 2:161-162]

{And whoever desires other than Islam as religion - never will it be accepted from him, and he, in the Hereafter, will be among the losers.} [Quran 2:85]

The good deeds that the disbelievers do in the worldly life will not avail them before Allaah The Almighty on the Day of Resurrection. Their disbelief and polytheism will outweigh all of their favorable deeds, for polytheism is the gravest injustice. Allaah The Almighty Says (what means):

{And [mention, O Muhammad], when Luqmaan said to his son while he was instructing him, "O my son, do not associate [anything] with Allaah. Indeed, association [with him] is great injustice."} [Quran 31:13]

{The heavens almost rupture therefrom and the earth splits open and the mountains collapse in devastation that they attribute to the Most Merciful a son.} [Quran 19:90-91]

Take note of how grave and heinous it is to believe in the Trinity, something for which the universal system almost disrupts at the very thought of. The good deeds of those who believe in the Trinity will not avail them while they abuse their Creator, seeking to cancel out the greatest fact of life: Tawheed (Islamic monotheism) only to believe in the most illogical doctrine.

On the other hand, the Jews, who as you said believe in one God, attributed evil characteristics to Allaah The Almighty, above which He is far Exalted. They attached poverty, fatigue and oblivion to Him. Allaah The Almighty Says (what means):

{And We did certainly create the heavens and earth and what is between them in six days, and there touched Us no weariness.} [Quran 50:38]

{Allaah has certainly heard the statement of those [Jews] who said, "Indeed, Allaah is poor, while we are rich."} [Quran 2:181]

{And the Jews say, "The hand of Allaah is chained."} [Quran 5:64]

The good deeds of the disbelievers will avail them nothing on the Day of Resurrection due to their disbelief; Allaah The Almighty Says (what means): {And We will regard what they have done of deeds and make them as dust dispersed.} [Quran 25:23]

Commenting on this verse, Ibn Katheer said that Allaah The Almighty will judge people according to their worldly deeds: whether good or evil. However, the good deeds of the disbelievers in this world will not avail them because they were either void of sincerity or not according to the Sharee‘ah. No act is acceptable if it is not based on the Sharee‘ah. The deeds of the disbelievers are blemished due to one of these two things. Once they are blemished by both factors, they are more liable to be rejected.

Ash-Shawkaani mentioned that the reason behind their deeds being rejected that were outwardly good, such as maintaining kinship relations and feeding the needy, is their disbelief (Kufr).

There are more verses that are similar to the above one. These include the following:

{The example of those who disbelieve in their Lord is [that] their deeds are like ashes which the wind blows forcefully on a stormy day.} [Quran 14:18]

{But those who disbelieved - their deeds are like a mirage in a lowland which a thirsty one thinks is water until, when he comes to it, he finds it is nothing.} [Quran 24:39]

This evidence is related to their treatment in the Hereafter, for reward then is conditional to Islam.

At the same time, Allaah The Almighty rewards the disbelievers for their good deeds in the worldly life. Indeed, He does not do injustice, [even] as much as an atom's weight. It is narrated that the Prophet, sallallaahu ‘alayhi wa sallam , said that the disbeliever is rewarded for his good deeds in the worldly life until he comes to Allaah The Almighty in the Hereafter with no good deeds. [Muslim]

Thereby, it is obvious that if a disbeliever does a good deed intending it for the sake Allaah The Almighty he will not die until he is rewarded for it. Then, he will come in the Hereafter with no deeds, for which he may obtain a reward.

Scholars have different points of view regarding the fate of those who heard about Islam but knew nothing about it.

Some scholars asserted that the people in question will not be excused. Others said that they will be excused until they are informed of the message beyond the excuse of ignorance. Those who advocate the second view are divided into two groups. One of them hold that such people will have their share of the mercy of Allaah The Almighty, for some of them lived and never heard of the name of the Prophet, sallallaahu ‘alayhi wa sallam, let alone his message; while others learned about the Prophet, sallallaahu ‘alayhi wa sallam, as a caller to Islam, but – and we seek refuge with Allaah from this – that he was not truthful. According to Al-Ghazzaali the people in both cases are to be excused. He added that anyone who knew about the religion of Islam and were near to the Muslims but despite that did not embrace Islam, is a disbeliever.

The other group of scholars said that people whom the message never reached are to be excused. They added that those people will be tested on the Day of Resurrection. The evidence of this is the Hadeeth which indicates that among those who will be tested on the Day of Resurrection is a man to whom no messengers of Allaah The Almighty were sent. Allaah The Almighty will take his pledge of obedience and then order him to enter into a fire. Once he enters, it will be cold and safe for him. If he refuses to enter it, he will be admitted into Hell that is prepared for the disbelievers. [Ahmad. At-Tabaraani: Al-Kabeer]

The last opinion was adopted by Ibn Hazm, Al-Bayhaqi, Ibn Taymiyyah, Ibnul-Qayyim, Ibn Katheer and Ibn Hajar . Abul-Hasan Al-Ash‘ari even said that this is the opinion of Ahlus-Sunnah (the Sunni mainstream).

Allaah Knows best.