Alright so first off, you don’t have a void setup() ? I think you should start with that 
void setup()
{
size(600,600);
}
Next, where is your levels variable? I see that you are using one. I will declare that at the top of your program:
int levels = 0;
Now, you will be able to pass in your variable through the switch statement.
Next, you have functions that aren’t really created? Like menu() or game() for example.
I went through and made simple backgrounds for each function here:
void menu()
{
background(0,255,0);
textAlign(CENTER);
textSize(50);
text("MENU", width/2,height/2);
}
void game()
{
background(255,255,0);
textAlign(CENTER);
textSize(50);
text("GAME", width/2,height/2);
}
void level2()
{
background(0,255,255);
textAlign(CENTER);
textSize(50);
text("LEVEL 2", width/2,height/2);
}
void level3()
{
background(255,155,255);
textAlign(CENTER);
textSize(50);
text("LEVEL 3", width/2,height/2);
}
void info()
{
background(125,255,255);
textAlign(CENTER);
textSize(50);
text("INFO", width/2,height/2);
}
Now, depending on the function called, you will see a different screen with whatever state it is on.
Next, I noticed in your void keyPressed() function you were switching the levels variable again? I don’t necessarily know exactly what your aim is with doing that, but what I did was change it so you’re switching the actual key? And changing the state based on that?
Like this:
void keyPressed() {
switch(key)
{
case 'q':
levels = 1; //press q to change the levels to 1
break;
case 'w':
levels = 2; //press w to change the levels to 2
break;
case 'e':
levels = 3; //press e to change the levels to 3
break;
case 'r':
levels = 4; //press r to change the levels to 4
break;
default:
levels = 0; //press anything else to change the levels back to 0
break;
}
}
As of now, you have a very simple state switching program. I kept everything that you had in draw, and just made those changes that I showed you. You can either use this, and expand on it, or you can use @TfGuy44’s code, which is another great example as well.
Feel free to keep us posted, and we would love to help you further,
EnhancedLoop7