Why voltage is the same after placing a resistor?
I'm using a Raspberry and on PIN 1 I have 3.3v at 0.076A. What I've
  did is very simple, I've connected a Resistor to my Raspberry voltage
  source, and I've connected the other side of the resistor to the
  multimeter and the multimeter to Raspberry GND pin.


So you have this:







simulate this circuit &ndash; Schematic created using CircuitLab

That is not how you measure a voltage, I mean you can, but usually you place the voltmeter in parallel to a component you want to measure the voltage across. What your approach does is increase your measurement error for measuring the voltage of Pin 1. With the configuration you used not by much.

The voltmeter is basically a big resistor (in the order of 1 MegaOhm or more), so in this configuration you have almost no current flowing. If you just switch to measuring ampere, the amperemeter is a very low resistance, so your circuit changes completely between the two modes.

So you might measure the voltage like this:







simulate this circuit

Now this will not teach you anything about Ohm's law in a useful way, just like your way didn't. Here everything is in parallel and the resistor doesn't have an influence on the voltage because the whole voltage will drop across the resistor. (in an ideal world, in the real world you will get a small drop of voltage because of the internal resistance inside your voltage source when you connect the resistor)

To study Ohm's law I suggest something like this:







simulate this circuit

Because now, the R3 will have an measurable impact on the voltage over R2. And you can change the values of R2 and R3 easily to check if your calculations are correct.