Do angels still manifest themselves as humans and appear to us without us knowing? Do the rabbinic sources have something to say about this?
I'm not familiar with sources that mention recent instances of this, but I do remember one post-Biblical instance in Shas of angels manifesting themselves as humans in Bavel in the days of the Amoraim.
See תענית כד עמ' ב
אֲמַר רַב מָרִי בְּרַהּ דְּבַת שְׁמוּאֵל: אֲנָא הֲוָה קָאֵימְנָא אַגּוּדָּא דִּנְהַר פָּפָּא, חֲזַאי לְמַלְאֲכֵי דְּאִידְּמוֹ לְמַלָּחֵי דְּקָא מַיְיתִי חָלָא וּמְלוֹנְהוּ לְאַרְבֵּי, וַהֲוָה קִמְחָא דִּסְמִידָא. אֲתוֹ כּוּלֵּי עָלְמָא לְמִיזְבַּן, אָמֵינָא לְהוּ: מֵהָא לָא תִּיזְבְּנוּן דְּמַעֲשֵׂה נִסִּים הוּא, לִמְחַר אָתְיָין אַרְבֵי דְּחִיטֵּי דְּפַרְזִינָא.
Translation of the segment in bold:
I saw angels who appeared as sailors bringing sand and filling ships with it, and it became fine flour.
(BTW - after first seeing this many years ago, I have long been fascinated by the phonetic similarity of מלאכי - angels, to מלחי, sailors of the salty sea)
The above would be a case of a standard מלאך השם to be viewed as some supernatural/spiritual creation of השם that He commands and acts on His behalf, and in this case of the Gemara they appear as humans. This as opposed to humans who attain the status of מלאך השם.
Angels exist, but angels refer to natural forces, “He makes His angels winds; His ministers flaming fire” (Psalms 104:4).
Rambam says that when angels are mentioned in Torah, the story must describe a vision, as angels do not exist in the physical existence. See Guide, Book II, CHAPTER XLII
Thus, angels cannot take on human form. Genesis 18:2 says, three men/angels visited Abraham. Where they angels or humans?
The word malakhim means messengers. Genesis 32:4 reports that Jacob sent malakhim to his brother Esau. Rashi maintains that Jacob sent angels. Rational thinkers say that he sent messengers. I think it is correct to translate the word as “messengers,” for they conveyed messages to Sarah and Lot. Angels are whatever fulfills the will of God. Even snow anf wind are angels. Thus, good humans may be called angels. The visitors to Abraham were good humans, not angels with wings. This is the only human form an angel can take.