I'm not a grammarian, but here's my take on "I was like whatever"
I - pronoun
Used to refer to oneself as speaker or writer.
was like - comes from the idiomatic phrase "be like"
be like - informal
To say or utter. Used chiefly in oral narration: "And he's like, "Leave me alone!"
Some linguists do call this "quotative like", though it's not a well-defined thing so far. Here's a long article by Prof. Dr. Isabelle Buchstaller, a variationist sociolinguist.
"And I’m Like, Read This!" article by Jessica Love.
The general consensus is that the quotative like encourages a speaker
to embody the participants in a conversation. Thus, the speaker
vocalizes the contents of participants’ utterances, but also her
attitudes toward those utterances. She can dramatize multiple
viewpoints, one after another, making it perfectly clear all the while
which views she sympathizes with and which she does not. Hear yourself
say these sentences aloud: I walked up to Randy and he was like, Why
are you late? I was like, Because you gave me the wrong time! You
have, in addition to relaying the he-says she-says bones of a
conversation, probably betrayed some moral indignation. Randy was
unreasonable, and you were in the right. It’s possible to do all this
with says, of course, but not nearly as naturally.
The quotative like is often followed by filler words like well or
dude, as in He was like, Dude, get your act together. Much like a mask
or good make-up or the right dialect coaching, these fillers further
distinguish the current speaker from the person (or earlier self)
being quoted. They give the performance a bit of flair. (And make no
mistake: far from indicating laziness, the quotative like can inspire
some great performances.)
whatever - interjection informal
Used to indicate indifference to or scorn for something, such as a remark or suggestion: We're having pizza tonight.— "Whatever. I don't care."