A few things struck me about these stories. First, The Call of Cthulhu is among the best remixes of anthropological tropes into a fantastical story that I've ever read. In that regard I would put it on par with the work of Ursula K. Le Guin (who I expect might not appreciate the comparison given Lovecraft's notorious racism, but anyway). Among Le Guin's stories, which I've read about six, I really like The Lathe of Heaven. It's a well told story that has some ideas worth pondering.
Back to Lovecraft, one thing that struck me is that both the stories I read seem interpretable on one level as just slightly disguised critique of Christianity. At least my casual google searching did not find this aspect of his writing mentioned in the literary commentary on his work. Both stories use a technique that elides ideas about extra-terrestrials with Christian theology and ideas about the demonic. Those three are sort of blended together, but to the ultimate effect of inverting core Christian theological or scriptural references from something positive (according to Christians) into something demonic. As the mystery unravels in The Call of Chthulhu, it finally culminates with the scene where Cthulhu is witnessed but his appearance is incomprehensible (it drives men mad). His island has impossible angles on it. He existed outside of our time and space. Really Cthulhu reads almost like a straightforwardly transposed vision of how many negative theologians, from Neoplatonists through Christians to Hindus and Daoists, talk about God. Negative theology is also called apophatic theology, and means theology that reasons about the divine through understanding what it is not, rather than affirming what it is. Last, Cthulhu will emerge from his tomb to liberate his cult followers, which would seem to parody ideas in from Christianity.
The Dunwich Horror is in some ways a simpler story and perhaps less elegant than Cthulhu. It reads a bit more like pulpy horror. It also contains a straightforward Christianity reference in its climax when the demonic extraterrestrial thing, in the process of being banished by the hero's of the story, from up on a hilltop calls out in suffering "Father" in a manner that is very reminiscent of the crucifixion scene. Here though the thing calling out is an extraterrestrial demon-spawn bent on the destruction of all life as we know it in order to repopulate the earth with incomprehensibly (to us) alien life forms.
A few thoughts I had reading this material is in my casual searching I didn't immediately notice literary criticism that had made much mention of these overt Christianity connections in Lovecraft's work. Lovecraft was an atheist, and at least in the two works I read, as I've described, these references are used as a parody or one might argue blasphemy of Christianity - which is clever because it makes them stories about blasphemy that also are themselves a different blasphemy. The religion connection, perhaps not appreciated, reminded me of the way the strong religion connection in Stoker's Dracula was not always appreciated. Dracula can be analyzed from all kinds of angles, but there's a very strong case to be made that at least for Stoker himself it was essentially a veiled pro-Catholic manifesto (Stoker may have been a closeted Catholic). Another curious parallel between the two is Stoker was also deeply racist - The Lair of the White Worm is one of the most racist novels I've ever read.
Thus, at one level these stories by Lovecraft struck me as rather straightforward, even if somewhat veiled, anti-religious manifestos, in much the way Stoker's Dracula is a pro-Catholic manifesto. The simple moral of Lovecraft's stories (at least the ones I read) is that to engage in any thought that seeks to transcend ordinary experience is to risk madness. Clearly the unique role of madness in Lovecraft's stories may be related to both of his parents having been committed to a mental institution.
A last thought I had about this material is that Lovecraft displays the a tendency I have noticed in other people who are primarily trained in physics (rather than in biology or social science) to take seriously the idea that extra-terrestrial lifeforms would transcend all human social and moral norms. Lovecraft stated this expressly:
Now all my tales are based on the fundamental premise that common human laws and interests and emotions have no validity or significance in the vast cosmos-at-large. To me there is nothing but puerility in a tale in which the human form--and the local human passions and conditions and standards--are depicted as native to other worlds or other universes. To achieve the essence of real externality, whether of time or space or dimension, one must forget that such things as organic life, good and evil, love and hate, and all such local attributes of a negligible and temporary race called mankind, have any existence at all. Only the human scenes and characters must have human qualities.
This quotation from Lovecraft is from his 1927 resubmission of The Call of Cthulhu to Weird Tales (as reported by S.T. Joshi)
Lovecraft appears to have been more well read in physics and astronomy than in evolutionary sciences. What I believe is an error in his logic is that the evolutionary sciences all point to cooperation dynamics as being fundamental to any kind of social life. To have cooperation you have to at least sometimes solve collective action problems (problems in which there are incentives to defect) and we know of only a narrow range of solutions that actually work for these problems in both the extensive mathematical theory on this subject and in the extensive studies of cooperation across the diversity of species on our planet. Basically you can count the number of fundamental collective action solutions that actually work on one hand. Solutions that don't work are legion. Perhaps this is why stories about "Human laws and interests and emotions" very frequently center of collective action: because it is hard to do, or, there are so many ways to try but fail. Speaking about this topic, in an interview I read probably 15 years ago with Steven Pinker he said it would be accurate to say that the moral rules 'exist' in the universe in a sense. That is, the universe is so structured that the only of intelligent things that exist are things that evolve to be intelligent, and they all therefore must face fundamentally similar collective action problems, and there are only a few solutions to these problems that work. In a talk I saw by space ethicist Kelly Smith (Clemson University) he once stated if he could send one book to extra-terrestrials he would send Kant's work on the categorical imperative, because he thought it encapsulated the moral rules that any social species inevitably would recognize - because they're the only moral rules that actually work.
The vast diversity of the cosmos, as best we currently know, would not mean encounters with extra-terrestrials actually would be transcendent. Perhaps it's disappointing to some, but all our evolutionary evidence suggests that social transcendence, even the evil kind envisioned by Lovecraft, will be found no where in our universe. Everything that is intelligent in our universe has to evolve its intelligence, which means it has to follow the same rules for how replicating intelligent things resolve their collective action problems.