Omens need to be felt and analyzed. Each omen is specific to a person. Many omens occur more than once before the actual event occurs letting the person know of the impending event. If we consider Duryodhan's omen described in the first post, https://en.wikipedia.org/wiki/Gandhari_(Mahabharata)#:~:text=After%20the%20birth%20of%20her,regarding%20his%20firstborn's%20possibility%20of

Firstly, Duryodhana's cries, followed by winds and fires and the howling of animals. Each of these events taken individually would not mean anything but stringing them together caused people to recognize the omen.

The way to recognize a omen is to become aware of a natural event which has a lower probability of happening. For example, when driving from one place to another, you might catch a couple of red lights. But if you catch a dozen red lights or more consecutively, then it is more probably an omen. Once you recognize this omen, you should be able to confirm it with other low probabilty events before the actual event happens.

What are omens? Omens are normal things which happen in everyday in normal life but could hold special meaning for you / your family. For example, one of the passages mentions that

As soon as Duryodhana was born, he began to cry and bray like an ass. And hearing that sound, the asses, vultures, jackals and crows uttered their respective cries responsively.

Taken individually, these are normal things which happen everyday. Any new baby cries and all the animals make sounds. But in this particular instance, the sages of the time interpreted it as an omen.

This omen pertains only to Duryodhana and his family. As such, most omens pertain only to one particular person / their family.