As in このオレさま and この僕も. I know the literal translation, but I never understand what the intent of it is.
I think この usually implies some quality of “me”. You can translate it as “someone like me”. You can insert some adjectives between この and <first person pronoun>.
Usually it sounds proud or arrogant, especially in このオレさま.
But as Hyperworm pointed out, it can be used in exactly the opposite sense. e.g.
I think この私 tends to refer to some positive quality, and こんな私 some negative quality. But I'm not sure.
"The guy standing here in front of you"
"This guy here"
"The guy you're looking at"
Some clarification as noted by the commenters. Yes, オレ and 僕 or course refer to the speaker. So the question is, what is the nuance introduced by the demonstrative adjective この? It is "this me", as opposed to some other "me", such as a "me" at some other point in time, or a hypothetical "me" in some other situation. Since "this me" is ungrammatical in English, we need some other word to stand in for "me", for which I chose "guy", although I suppose there are equally good alternatives. Another way of introducing this nuance would be with a formulation such as "right now I..." or "standing here I...".
kono = proximal to the speaker
This kind of deictic meaning is not restricted to kono, sono, and ano. There are at least these additional forms:
adnominals: kono, konna [emphatic]
This type of deixis is expressed by the entire paradigm, and not only by kono, sono, and ano.
Speakers are always proximal to themselves. Hence, one must use kono with a pronominal expression referring to the 1st person.
However, kono itself does not express meaning in the modesty-respect dimension. This dimension is referenced by the pronominal expression: 俺 is far less modest than 私, and that leads to the differing nuances of この俺 and この私.