Nobs are the big guys you see starting on the second mission that take a metric ton of damage before finally going into a 'stunned' state where they may be killed. They deal massive damage in melee, so unless you activate FURY, it would be best to engage them at range.
Starting around Chapters 6 and 7, you will start seeing Shoota Nobs, these Nobs are simply a larger version of the basic Shoota Boyz. Shoot them as normal while you can, and when you see them pause to reload their guns or to unjam their guns, charge forwards and engage them in melee.
Once they are stunned, aproach them and press to enter a button mashing sequence to execute them and regain any health you may have lost in the fight.