... but I'm sure you want slightly more detail, so let me expound:
You're getting a lot of good advice about balance, about old-school methods, about optimized builds to mitigate the balance, and I'm actually surprised to not (yet) see one about CR numbers and linking to Wolfram Alpha, but I'm sure it's coming. And this is all great, fantastic advice. Read it, and the other answers. But my response to your question--and it will contain an answer--is...
Are you serious?!
No really, are you freaking serious? Because what I'm reading is that you have a rare, golden opportunity to have an especially unique campaign, and you're asking if you should go with it.
Dude, White Wolf has made an entire game line based on this premise, called "Mage: the Pretentious Edition-Specific Subtitle." And if you can get past the scent of patchouli reeking off the writing, it's actually really good.
What's so great about it is that everything in the game serves to remind you that magic is real, it is distinct, it is unique (especially the newer edition of Mage, whose setting is sadly poorer), it is everywhere, and it is not just an appliance you use for a simple end.
"But my players just want to kill things and take their stuff!"
Bullshit. They had a thousand and one options, and they all decided to make magical characters. And even if they made them in isolation, it appears that they even kept the choice after finding out the others also made magical characters. Given the options in 5e, any one of them could have said, "well, magic is going to be overdone, but I still like the supernatural stuff... so maybe an Avenger Paladin like a medieval Batman, or an Arcane Trickster modeled after this Naruto character I liked when I was a kid, or maybe a crazy Bard with grappling feats who I play as Rowdy Roddy Piper--I'm not even joking he IS Rowdy Roddy Piper and he's all out of bubblegum, yes!!"
No, they stuck with it. All deep, hardcore magical classes.
"Are you sure?"
Yes, but you might give The Same Page Tool a try to make sure everyone's on the page. You probably should do this anyway. So go do that.
"OK, you were right, now what?"
I know I was, thanks. So, let me give it to you straight: It's going to take a lot of work, and this may be a little above your comfort zone as a new DM. You sound awesome, but it may be above even your skill level right now. I'm not going to assume that though. Let's assume success is an option!
Consider house ruling a few things from the top. Let me suggest 3 things to help you integrate magic into the very air your characters will breathe. They aren't necessarily the right answer, but they should get you thinking down the right path.
Draconic Sorcerer has Detect Magic going, constantly. No rolls, no concentration, it's part of who he is, the result of being a magical bloodline--a bit like Peter Parker's Spider Sense. You will need to add in magical details. Note objects that stand out "magically," and consider that spirits, the emotional energies poured into artwork, and sentimental value may be things that can ping this sense. You may want to do some research about auras and what the colours mean. That way you can describe any given object/person/etc as glowing with this or that colour, or whatever. They can analyze the results of this sense by rolling Arcana (or Religion if they don't have that, or maybe Insight--it's part of who they are, after all).
The Druid can sense all the living things within 30 feet, again, as part of who they are. Pick a sense and base it off that. Let's not do sight, that's the Draconic Sorcerer's thing, let's be crazy and do smell. In the middle of a jungle, the Druid may actually feel a mildly uncomfortable pressure due to the absolute weight of life around them. In a desert, however, the slightest life would stand out like a pinprick. A moldy dungeon may feel slightly tingly; petting a horse is going to feel very pleasant, almost like the horse is petting the Druid--unless the horse is undead. Pick a key feeling for plants (tingling?), a key feeling for animals (throbbing?), and a key feeling for sentients (thrumming as if you were a guitar string) to describe things with. A Nature (or Arcana if it's a weird Druid without the Nature proficiency, or Religion failing even that) roll can analyze those sensations for more detail.
For the Warlock, since you didn't describe which kind, let's go with sound. Once more, this is an innate part of this magically transformed person; like the others, you can no sooner remove this than remove their emotions. But let's not just rip off the previous examples and go with any old sound. What makes a Warlock is that they have some form of patron... so this is going to be a voice. The Archfey will narrate things, like the narrator in The Stanley Parable or in the movie Stranger Than Fiction. If the patron is The Fiend, then instead perhaps the Fiend will whisper in their ear, like a cartoon devil on the character's shoulder--in fact, go ahead and make the Fiend show up as a cartoon devil that only this character can see. Or, if the character is affected by the Great Old One, then give them auditory hallucinations of nightmarish secrets spoken in words no sane mind can comprehend, but hinting at the secrets that lie beneath--the lies, the manipulations, the arcane and hidden about things. Once again, choose Arcana, Religion, or perhaps Investigation as the go-to proficiency for interpreting more from this sense.
As a slight alternate, instead of allowing them to roll a skill to go deeper, allow them to roll that skill to "proc" or fire off that sense. Perhaps it doesn't even appear unless they succeed. Or just base the quality of the information off of the level of success/failure.
A Lot of Work
That's my simplest advice, but it's going to take a lot of work. I know, I understand. But it's going to be so immersive, my friend. More so than adjusting CRs based on the ratio of monster to PC hit points. More so than forcing your players to perform 30 minutes of data entry to make a new character every time they or you make a mistake. This is especially true if you make those senses part of your descriptions and interaction, and if you make those senses also a liability. The pressure of the living could be quite debilitating if the Druid is infected with some form of evil spores (which a Warlock of the Great Old One could know a way to help with, thus giving you an innate adventure hook). The Fiend may whisper very bad ideas in the Warlock's ear, ideas which seem good at the time. And a sufficiently magical object may blind the Draconic Sorcerer's actual visible-spectrum vision.
But don't focus too much on the weaknesses. Focus on what they can add.
These senses can make up for the lack of other classes' capabilities.
The Archfey Warlock's narrating patron can outright say, in the right circumstances, "... but the constable's family isn't nearly so capable of protecting themselves, and he knows it," to help with an Intimidation attempt that may well fail for lack of a charismatic Rogue. The Druid can feel the life draining out of creatures, or sense the presence of living creatures lying in ambush, making up for a lack of a Ranger. The keen magical senses of the Dragonborn can identify vulnerabilities in monsters--especially if you add strong ones for him to find. Perhaps all goblins are deathly allergic to milk, or the undead are burned by salt.
So that's it, that's my advice with examples on not only whether you should tailor encounters, but how. In short:
You have magical characters, so make magic an integral--no, the integral part of your world. Do so, and especially as you get used to it and comfortable with house rules and adjudicating on the fly, your campaign will be the most memorable of all.
And all because your players were too stubborn to make a balanced party.