I would like to add that 'portion' could have the meaning of a certain amount of food served to one person and is considered in that particular sense as a whole individual quantity but still relatively as part of the meal.
Another literary sense of 'portion' refers to one's overall circumstances or conditions in life. The meaning here completely deviates from that of 'part'.
A 'component ' is a 'part' of a whole (be it a machine, system etc..) that partly constitutes and forms it.
In Mathematics it refers to one of the objects or numbers that together constitute a set,in other words a connected subset of a set.
In chemistry 'component' refers to an individual piece or a complete assembly of individual pieces that are capable of being joined with other pieces to form a whole.
In some readings you will come across ' component part',where the precise concrete meaning of 'component' as a constituent becomes clear.
A 'portion' is a 'part' as well, yet its sense is marked by 'division', 'allocation' or 'separation' of this part.
As an example you can say 'part of a building' is painted ,but you can never interchange it with 'portion',because the painted part is not segregated.
It is true that 'part' is a very general definition that includes many other terms such as 'portion' ,'component','segment' ,'fraction' ,'element' ,'constituent' etc... and they could all be interchanged by the word 'part' as a more generalized term, but for specification they will be used to give a more precise and concrete meaning.
The fine differences and the accurate usages of such terms has to be identified first by definition as you required in your question , then by practice you will be able to use them unpremeditatedly .