These are the three most prevalent themes in the game.
Water is, while not as anvilicious as Downpour, an obvious one. Alex encounters water many times, usually with monsters hiding under the surface, representing "memories just beneath the surface", and then there is of course the method of sacrifice for his family and what happened to Josh.
Spiders are much easier to see as a theme; aside from their various appearances in the game (crawling in the walls of the Grand Hotel, the picture in the playground), the bosses most clearly resemble spiders. Sepulcher hangs upside down from a web of wires connected to flesh, and in addition comes out of a hole in the ground like a trapdoor spider, and lastly is found in a greenhouse, basically a giant garden. Scarlet has extremely long limbs and crawls around much like a spider over the floor, walls, and ceiling in the second half of her battle. Asphyxia is quite clear with multiple limbs carrying it around. Amnion is the most blatant, designed to resemble a giant spider in many ways. There is also the enemies like the Needlers. The reason spiders are so very prevalent is up for debate.
Finally birth is a large theme in the game, with the bosses again having something to say about it. Along with the vagina dentata-esque mouths of the Schism and the Lurker and the head peering out from the groin of the Needler, the boss Sepulcher comes out of, again, a hole in the ground and the sacs of flesh keeping it suspended may represent an umbilical cord. Scarlet rises naked from a bloody portal in the ground with her arms around the doctor/father rather than the other way around, and gazes at Fitch as a mother might look at a child before biting his head off. Asphyxia comes out of very vagina-esque portals in the walls. Amnion resembles a pregnant woman, and a child comes out of it when it is defeated. Lillian Shepherd's death may also mock birth—strapped down, Lillian is torn in half at her waist, and dies.
Christian imagery and connections
The bosses can draw surprising connections to the Christian religion. Joseph Bartlett, Joseph being a prominent name in Christianity and the father of Jesus, is resurrected from a tree where the character first starts to learn of the evils happening and what's really going on, possibly representing the Tree of Life or the Tree of Knowledge of Good and Evil in the garden of Eden—keep in mind Alex and Mayor Bartlett are in the town's greenhouse at the time. What's more, Sepulcher, the monstrous form of Joey, is upside down—disciples of Jesus asked to be crucified upside down when martyred, because they weren't worthy to be crucified in the same manner as Jesus.
Scarlet is a porcelain doll with flesh underneath born from a pool of blood; now think of communion. Bible quotes from Jesus read at communion read: "This is my body, which is broken for you"—Scarlet was sacrificed to keep the town safe, and moreover, you have to physically break apart the flesh on the monstrous doll. It then goes on to say "This is my blood, drink, do this as often in remembrance of me"—Scarlet's father, Fitch, was cutting himself in guilt over killing his dauther, and refers to it as "bleeding out the sin".
Asphyxia is a monster summoned from a suffocated child, and she can breathe a poisonous gas at you. One of the earliest passages in the Bible describes the creation of man as God "breathing the breath of life into Adam". Asphyxia is the opposite—upon being forced to breathe, she dies.
Amnion is a bit more difficult to decipher, but may have a connection to Cain and Abel. Joshua is the Abel in the relationship, if for no other reason than he wasn't a dick to Alex. Alex is the Cain; while he was respectful and did his duty, he was overcome with jealousy for the favor his brother had, and ended up killing him. In the Bible, God rages at Cain, saying "the earth cries out with the blood of your brother". Amnion's mouth is blocked by a strange device hooked into its mouth (And like Abel, Josh is dead in case you didn't catch that), and yet he still screams at Alex as you fight the boss. This mimics Abel's death screaming at Cain in the Bible.
There is also cross-shaped torture rack Lillian Shepherd is strapped to. Relating even further, see above at her entry in relation to birth. God punished Eve for her sin by making birth painful for her and all women, strengthening the symbolism. Giving birth to Alex would have been doubly painful with Lillian knowing she had to kill him later.