Elisa's Scars
Elisa's lack of voice is linked to the three scars she has on each side of her neck. On one hand, they seem like deliberate cuts and represent the strange, horrific human capacity for cruel violence that we see Strickland displaying constantly. On the other, they resemble gills and give her a connection with the creature she falls in love with. At the end of the film, they do indeed turn into gills.
Key Lime Pie
Giles makes Elisa get key lime pie with him at the pie shop where a man he has a crush on works. Back at Giles's apartment, Elisa can barely eat the pie and spits it out. Giles doesn't want to see it go to waste, so he goes to put it in his fridge, which is entirely full of slices of key lime pie. It represents Giles' desire for the things that are bad for him, such as that pie shop clerk who ultimately is revealed to be a homophobe.
Strickland's Cattle Prod
Strickland uses an electrified cattle prod to torture the creature and intimidate everyone that he works with. It's a phallic symbol, and therefore a totem of Strickland's violent and toxic masculinity. But it's also a barbaric weapon, and clearly this speaks to the pleasure Strickland gets from enacting violence.
The Security Camera
Around the time that the movie is set, the security camera and closed-circuit television would have been relatively new inventions. In terms of the story, the camera represents centralized surveillance, as the closed-circuit television in the lab facility is one of Strickland's method of asserting power and control over the secret government operation. Filmically, the security cameras are a spin on the very cameras used to shoot movies, and the fact that the characters redirect the security camera and generally use it to undermine Strickland gives them a kind of power that the characters on camera rarely have in movies. The security camera is also a phallic object and something that "shoots" much like the guns used at the end of the film.
