I wonder whether Judaism teaches that those unbelievers or those who are Jews but nevertheless lead a sinful life would go to hell someday when judgement time comes.
If by "unbelievers" you mean those who are not Jewish, then the answer is "no". The Talmud at Sanhedrin 105a says that the righteous of all nations shall have a place in the world to come. The question is "who is righteous?" As noted, a gentile who keeps the seven Noachide laws in all of their details is said to have attained the level of righteousness of the High Priest in Temple times. Baba Kamma 38a. Maimonides (the "Rambam") at Hilchot Melakim 8:11 confirmed that a gentile fully-observant of the Noachide laws has a place in the world to come.
If by "unbelievers" you are referring to apostate, atheistic, or agnostic Jews, then the answer is "it depends." If the person is an atheist or agnostic because he's never had an introduction to Judaism or knows what the commandments are, much less how to observe them, he could not be judged guilty for violating laws he did not know. On the other hand, someone who is especially sinful, and more so, one who causes others to sin, e.g. an adulterer or one who embarrasses others, according to some views, are doomed in Gehinnom forever. Baba Metzia 58b.
Another view, that of Hillel, is that (as Shalom noted) that the worst of sinners will suffer in Gehinnom for 12 months and then their souls will be destroyed into dust that will blanket Heaven and be walked upon by the righteous. Rosh Hashana 17a. Less aggregious sinners, however, will spend no more than 12 months in Gehinnom and then be raised up to Heaven. Ibid.
In addition, there is a view that eternal punishment exists for those who attack and defame Rabbinic Law. It is said that they will be boiled in feces for eternity. Gittin 57a. Which of these views is correct, no one is sure. The purpose of such speculation appears to be to motivate Jews towards certain behaviors rather than giving you a precise picture of what to expect.
There are many different views on these matters. The Rambam in Moreh Nevuchim seems to take an original view that there is no such thing as hell. The righteous and wise will reach a level where their soul continues after death, but the wicked will cease to exist. The Rambam seems to hold that those who do not have the right beliefs will not be able to be continue to exist for eternity. On the other hand, if someone sinned but overall was righteous, then he should be able to acquire olam haba.
In a word: no.
You're using a great deal of Christian wording here, so let me state the way it's phrased from a Jewish perspective, and hopefully this helps:
Barring some truly extreme cases, hell only lasts a maximum of twelve months before a soul can move on to higher realms.
Jews believe that all Jews, except for a few special cases, have a share in the World To Come; as do righteous non-Jews.
Recall that Judaism doesn't expect non-Jews to keep Judaism, just the Seven Noahide Laws.