In these examples, the messenger or angel of the Lord acts as an intermediary between God and humanity. It essentially acts as a representative or stand-in for God.
(ב) וְהוּא בְאֶחָד וּמִי יְשִׁיבֶנּוּ וְנַפְשׁוֹ אִוְּתָה וַיָּעַשׂ (איוב כג, יג), תָּנָא אֵין מַלְאָךְ אֶחָד עוֹשֶׂה שְׁתֵּי שְׁלִיחוֹת, וְלֹא שְׁנֵי מַלְאָכִים עוֹשִׂים שְׁלִיחוּת אֶחָת, וְאַתְּ אֲמַרְתְּ שְׁנֵי, אֶלָּא מִיכָאֵל אָמַר בְּשׂוֹרָתוֹ וְנִסְתַּלֵּק, גַּבְרִיאֵל נִשְׁתַּלַּח לַהֲפֹךְ אֶת סְדוֹם, וּרְפָאֵל לְהַצִּיל אֶת לוֹט. (בראשית יט, א): וַיָּבֹאוּ שְׁנֵי הַמַּלְאָכִים סְדֹמָה, הָכָא אַתְּ אָמַר מַלְאָכִים וּלְהַלָּן (בראשית יח, ב): קוֹרֵא אוֹתָן אֲנָשִׁים, אֶלָּא לְהַלָּן שֶׁהָיְתָה שְׁכִינָה עַל גַּבֵּיהֶן קְרָאָם אֲנָשִׁים, כֵּיוָן שֶׁנִּסְתַּלְּקָה שְׁכִינָה מֵעַל גַּבֵּיהֶן לָבְשׁוּ מַלְאָכוּת. אָמַר רַבִּי תַּנְחוּמָא אָמַר רַבִּי לֵוִי אַבְרָהָם שֶׁהָיָה כֹּחוֹ יָפֶה נִדְמוּ לוֹ בִּדְמוּת אֲנָשִׁים, אֲבָל לוֹט עַל יְדֵי שֶׁהָיָה כֹּחוֹ רַע נִדְמוּ לוֹ בִּדְמוּת מַלְאָכִים. אָמַר רַבִּי חֲנִינָא עַד שֶׁלֹא עָשׂוּ שְׁלִיחוּתָן קְרָאָן אֲנָשִׁים מִשֶּׁעָשׂוּ שְׁלִיחוּתָן מַלְאָכִים. אָמַר רַבִּי תַּנְחוּמָא לְאֶחָד שֶׁנָּטַל הֶגְמוֹנְיָא מִן הַמֶּלֶךְ, עַד שֶׁלֹא הִגִּיעַ לְבֵית אוֹרְיָין שֶׁלּוֹ הָיָה מְהַלֵּךְ כְּפַגָּן, כֵּיוָן שֶׁהִגִּיעַ לְבֵית אוֹרְיָין שֶׁלּוֹ הָיָה מְהַלֵּךְ כְּקָאלְמִין, כָּךְ עַד שֶׁלֹא עָשׂוּ שְׁלִיחוּתָן קְרָאָן אֲנָשִׁים כֵּיוָן שֶׁעָשׂוּ שְׁלִיחוּתָן קְרָאָן מַלְאָכִים.
(2) "But He is at one with Himself, and who can turn him? And what His soul desireth, even that He doeth." (Job 23:13) It was taught: One angel does not carry out two commissions, and two angels do not carry out one commission. And you say "two"!? (Genesis 19:1) Rather, Michael said his tidings and departed, Gabriel was sent to overthrow Sodom, and Raphael to rescue Lot.
Rashi describes here that angels are given a single task to carry out by God. His explanation is an attempt to explain why there are three men/angels in Genesis 18, but only two men/angels in Genesis 19. The angel who announces the birth of Isaac to Sara is no longer present in Genesis 19 because he has fulfilled his task.
(2) Looking up, he saw three men standing near him. As soon as he saw them, he ran from the entrance of the tent to greet them and, bowing to the ground,
(1) The two angels arrived in Sodom in the evening, as Lot was sitting in the gate of Sodom. When Lot saw them, he rose to greet them and, bowing low with his face to the ground, (2) he said, “Please, my lords, turn aside to your servant’s house to spend the night, and bathe your feet; then you may be on your way early.” But they said, “No, we will spend the night in the square.”
(23) That same night he arose, and taking his two wives, his two maidservants, and his eleven children, he crossed the ford of the Jabbok. (24) After taking them across the stream, he sent across all his possessions. (25) Jacob was left alone. And a man wrestled with him until the break of dawn. (26) When he saw that he had not prevailed against him, he wrenched Jacob’s hip at its socket, so that the socket of his hip was strained as he wrestled with him. (27) Then he said, “Let me go, for dawn is breaking.” But he answered, “I will not let you go, unless you bless me.” (28) Said the other, “What is your name?” He replied, “Jacob.” (29) Said he, “Your name shall no longer be Jacob, but Israel, for you have striven with beings divine and human, and have prevailed.” (30) Jacob asked, “Pray tell me your name.” But he said, “You must not ask my name!” And he took leave of him there. (31) So Jacob named the place Peniel, meaning, “I have seen a divine being face to face, yet my life has been preserved.” (32) The sun rose upon him as he passed Penuel, limping on his hip.
(1) In the year that King Uzziah died, I beheld my Lord seated on a high and lofty throne; and the skirts of His robe filled the Temple. (2) Seraphs stood in attendance on Him. Each of them had six wings: with two he covered his face, with two he covered his legs, and with two he would fly. (3) And one would call to the other, “Holy, holy, holy! The LORD of Hosts! His presence fills all the earth!” (4) The doorposts would shake at the sound of the one who called, and the House kept filling with smoke.
(4) I looked, and lo, a stormy wind came sweeping out of the north—a huge cloud and flashing fire, surrounded by a radiance; and in the center of it, in the center of the fire, a gleam as of amber. (5) In the center of it were also the figures of four creatures. And this was their appearance: They had the figures of human beings. (6) However, each had four faces, and each of them had four wings; (7) the legs of each were [fused into] a single rigid leg, and the feet of each were like a single calf’s hoof; and their sparkle was like the luster of burnished bronze. (8) They had human hands below their wings. The four of them had their faces and their wings on their four sides. (9) Each one’s wings touched those of the other. They did not turn when they moved; each could move in the direction of any of its faces. (10) Each of them had a human face [at the front]; each of the four had the face of a lion on the right; each of the four had the face of an ox on the left; and each of the four had the face of an eagle [at the back]. (11) Such were their faces. As for their wings, they were separated: above, each had two touching those of the others, while the other two covered its body. (12) And each could move in the direction of any of its faces; they went wherever the spirit impelled them to go, without turning when they moved.