The one at 2:06 is a natural harmonic hit with the bar depressed, and then allowed to return to pitch. At 5:20, a regular note is fading out, but generating a feedback loop. This is done with high gain and high volume (in-room) – this cannot be done with headphones or direct input, and it also can’t be done if you’re using a drop pedal or similarly using signal processing to alter pitch. It is the result of a vibration being produced by the guitar, amplified through the amp and speaker, and that output going back into the guitar’s pickup. It can be accomplished at lower volumes by holding the guitar with the pickup close to and facing the speaker cone you’re pushing sound through.
This can be done with a Sustainiac, but that is by NO MEANS required, and you will definitely be able to do it with a Strat, as long as you’re playing with high gain and at a good in-room volume.