The term "sons of G-d" בני האלהים is found 5 times in the Hebrew Bible, once in Genesis (6:2), three times in Job (1:6, 2:1 and 38:7) and one time in Psalms (29:1). What does it mean? Does it have the same meaning in both instances? What is it referring to? What are the different beliefs held about what this means? The Septuagint translates this both times as "sons of G-d". It's first used in Genesis 6 when the "sons of G-d" came and had relations with women. Then it's used again in the book of Job when all of the "sons of G-d" cheered at the creation of the earth in Genesis (Obviously means Angels here, correct? -or?). It's the same word used in both instances, and translated the same in the Septuagint in both instances. I just wanna learn.
See the discussion on the name elohim. The commentaries on Genesis discuss what was going on there; the simplest explanation is "the sons of the authorities", or "the sons of the powerful" or "the sons of judges" went and took [advantage of] any woman they wanted.
According to this translation (based on Rashi's commentary) in the first instance it means the children of the powerful (sons of the nobles).
According to the same site, the Iyov (Job) references are to angels.
There are three different concepts being brought in these citations that you bring. They all relate, but convey very different messages.
First of all, you are asking about "sons of god" (בני האלהים). Your reference to Tehillim (psalms), does not use that Hebrew term. So strictly speaking, there are only four references, not five. But the commentaries to Tehillim do associate the term בני אלים to one of the meanings relating to the usage in Genesis.
In Genesis 6:2, the Targum Onkelos (a classic commentator who translates the Hebrew to Aramaic) translates this phrase as בני רברביא, which means the children of legal scholars and judges or the children of princes meaning the aristocracy. Taken in context, this helps to explain what is going on here. These individuals have sexual relations with the daughters of HaAdam. The Targum translates this as בנת אנשא which means literally the daughters of enosh. There are several different terms used to describe human beings. The term enosh means someone who has not perfected themselves either intellectually or emotionally. They are unrefined and simple people.
And so, this text is describing how the children of the aristocrats and legal scholars were having sexual relations with these daughters of commoners.
And this follows the explanations of other classical commentators Targum Yonaton, Ramban and Rabbeinu Bechaye who explain that these people were judges of the people and they took sexual favors by force in the cases dealing with the non-aristocrats. It was a kind of bribery and was an accepted practice in that society.
This relates to a concept of what is commonly called marrying down or ניחות דרגה in Hebrew.
Rabbeinu Bechaye on Genesis 5:2 identifies these judges, the בני אלהים, as the descendants of Chava, Adam's wife and the Nachash HaKadmoni (a term which means literally the Primordial Serpent, but in the context of Rabbeinu Bechaye seems to mean an actual person).
After Kayin murdered his brother Hevel (Abel), Adam and Chava divorced (they parted company) for 130 years. These children from Chava and the Nachash HaKadmoni had such names as Yechavi'el and Metusha'el which is a naming convention normally reserved to Heavenly Angels. Rabbeinu Bechaye also counts Chanoch ben Kayin (Chanoch, son of of Cain, Genesis 4:17) among them. But in context, the naming convention is used here to indicate that they were aristocrats.
These aristocrats were those children outside of the family line from Seth שת, the third son of Adam and Chava (Genesis 4:25) who took the place of Hevel (הבל Abel, Genesis 4:2) who had been murdered by Kayin, his brother. Adam and Chava remarried after being apart for 130 years.
Rabbeinu Bechaye explains that this is the origin and meaning of the phrase Foundation Stone meaning אבן שתיה. The stone which serves as the foundation of the Temple in Jerusalem are the descendants of Seth.
This is the Peshat meaning of this text according to the Meforshim.
Strangely enough, this story from the Torah which included Chanoch ben Kayin also appears to be the source for the creation of the character, Superman. the Superman character is also blended with the Midrash Sefer Chanoch of Chanoch ben Yered (Genesis 5:18)
This comic was created by two American Jews from Cleveland, Ohio in 1933.
The comic creators, Jerry Siegel & Joe Shuster made their character come to Earth from the heavens with super powers to defend the innocent people of Earth from the powerful, evil ones. Superman's true name is Kal-El and his father's name is Jor-El, names using the Angel naming convention like mentioned by Rabbeinu Bechaye. And Superman comes to Earth from the heavens and falls in love with a human female, Lois Lane. Superman's Fortress of Solitude, which was originally called the Secret Citadel is located in the desolate north surrounded by snow which also parallels the details of the isolated tower that Chanoch would retreat to as found in Sefer Chanoch.
There are midrashic explanations which talk about these B'nai HaElohim being actual Angels. But in those discussions it emphasizes that the meaning in the Midrash is to show that everything which takes place here on a physical plane also occurs on the spiritual plane.
This parallel idea is also used in your citation from Tehillim 29:1. Rashi says B'nai Elim are the children of princes, meaning aristocrats. While Ibn Ezra says the term is referencing the stars, because that is the system which G-d has put in place for His influence to be made in the world generally.
The citations from Job (Iyov) are about actual Angels. This is confirmed from the Targum to Job 1:6 and 2:1 which translates this as כתי מלאכיא, which means types of Angels. Metzudot Tzion says this same usage also applies to Job 38:7. He explains that they are called B'nai HaElokim because they are close to the Shechina, G-d's revealed presence like members of His household. In the first two posukim from Job, both the Targum and Ramban explain that this was describing Rosh HaShanah (New Year), the time when G-d judges the whole world. These were the two categories of Angels that come before the Creator, one to advocate and the other to prosecute. This second category includes the Satan (which means literally Prosecutor or Accuser). The Ramban emphasizes that based on this information it is clear that this all transpired via prophecy, meaning Heavenly inspired vision, not in a physical sense.
So the term בני האלהים has multiple meanings and are dependent on context. It can be referring to children of aristocrats or children of judges or it can be referring to the family line from Chava other than the descendants of Seth, or it can be referring to actual Angels. To understand the correct meaning requires relying on the traditional teachings that have been preserved and passed down to the Jewish people.
If you accept Pirkei DeRabbi Eliezer, Chapter XXII, then all instances can mean the angels:
R. Dovid Zvi Hoffmann in his commentary to Bereshis summarizes different meanings and interpretations to bnei elohim. Based on that, and given that elohim has multiple meanings as mentioned here by others, one of the meforshim that seems to be the most plausible to the characterization of angelic beings and noble ones (imho) is Malbim since the idea of people claiming to be demigods, who ruled over others by virtue of their physical strength or status has been well documented in history.
Partial answer, to be updated bli neder soon
Midrash Rabbah to the passage in Bereishis seems bothered by your question. It gives two explanations of the phrase. As @Shalom said, one explanation is sons of the powerful, and thus Elohim is not a name of Hashem but rather a name of strength and power. The other explanation does indeed take Elokim here as a name of Hashem, and the phrase metaphorically refers to angels that Hashem kicked out of Shamayim. Not being allowed back upstairs, they decided to do whatever down here.
I currently don't have a hard source for the ones in Iyov and Tehillim, but it seems to me that all the ones in Iyov have to be referring to the angels (no, auto-correct, I'm not talking about the baseball team), but I could hear either translation in the passuk in Tehillim.