Lets make it pashut…
Greasy usually means the guys skin or hair is greasy and oily, which is usually because of lack of showering. Usually an ultra masmid yeshivish guy who has “no time” to shower will get the term greasy. He will look like and probably smell like he hasnt showered in a number of days. He will look spaced out and probably will be lost in thought thinking about some Reb Baruch Ber on a shvere sugya….
His English will be mostly Yeshivishe Shprach with a few mispronounced English words thrown in for good measure. He may have poor posture and stand hunched over.