$display vs $strobe vs $monitor in verilog?

I’ll be nice and summarize the LRM (Language Reference Manual), but you should read it. Everything is in IEEE Std 1800-2012 § 21.2 Display system tasks (Technically SystemVerilog, but these functions are identical.)

• $display : print the immediate values
  • § 21.2.1 The display and write tasks
• $strobe : print the values at the end of the current timestep
  • § 21.2.2 Strobed monitoring
• $monitor : print the values at the end of the current timestep if any values changed. $monitor can only be called once; sequential call will override the previous.
  • § 21.2.3 Continuous monitoring
• $write : same as $display but doesn’t terminate with a newline (\n)
  • § 21.2.1 The display and write tasks

Example:

reg [3:0] a,b;
integer i;
initial begin
  $monitor("monitor a:%h b:%h @ %0t", a, b, $time);
  for(i=0; i<4; i=i+1) begin
    $strobe("strobe  a:%h b:%h @ %0t", a, b, $time);
    $display("display a:%h b:%h @ %0t", a, b, $time);
    case(i)
      0 : a = 4;
      1 : b = 1;
      2 : begin end // do nothing
      3 : {a,b} = 9;
    endcase
    $display("display a:%h b:%h @ %0t", a, b, $time);
    #1;
  end
end

Outputs: (notice the print order and that monitor is not displayed at time 2)

display a:x b:x @ 0
display a:4 b:x @ 0
monitor a:4 b:x @ 0
strobe a:4 b:x @ 0
display a:4 b:x @ 1
display a:4 b:1 @ 1
monitor a:4 b:1 @ 1
strobe a:4 b:1 @ 1
display a:4 b:1 @ 2
display a:4 b:1 @ 2
strobe a:4 b:1 @ 2
display a:4 b:1 @ 3
display a:0 b:9 @ 3
monitor a:0 b:9 @ 3
strobe a:0 b:9 @ 3