These are all examples of a typical pop tenor voice. Usually it is about 80% tone and 20% aspirate (breathy) sound - this gives it the "raspy" sound that is so popular. Some people do awful things to themselves in order to produce those sounds (like smoking or drinking excessively) while others will scream until their voice reaches the desired hoarseness. These are all ineffective solutions.
Really the aspirate (breathy) sound occurs as a result of inefficient vocal production; not too hard to achieve since pop music vocal style typically incorporates inefficient vocal production anyway.
"Breathyness" is furthered accentuated in post-production mixing / mastering, and so the end result serves - at times - as an unrealistic model for people to look to (much in the same way glamor magazines sensationalize unrealistic portrayals of beauty.)
Honestly, this type of vocal production is obtainable with little practice and effort - vocal timbre doesn't necessarily have to be warm - Bob Dylan / Tom Petty / John Mellencamp are all examples of that enough.
To answer your last question directly - yes, you never want to strain your voice. That is bad. Straining your voice is bad for your voice...that's why it's called straining your voice.
All of that said, it is important to note that I am not suggesting the "pop tenor" style is lesser than other styles. I refer to it as inefficient in comparison to classical operatic style which focuses on creating maximum richness and resonance with zero aspiration.
There are many, many voice classifications, and "pop tenor" is not necessarily standard. Most would probably say "tenor" and I added the "pop" prefix merely to denote style. All would likely agree that all four videos suggest untrained voices. Again, not a bad thing, but something to keep in mind if you are studying how to produce these sounds for yourself.
Hope that helps.