Pursuing an activity to the exclusion of all else. The activity could be: driving non-stop, studying all night or longer, going on a drug jag or just about anything else.
I need to get home. No rest stops for me. I'll be straight running to Boston.
I didn't study my Sociology all semester. I'll be straight running for two days before the final.
That guy should get help. He's been straight running on junk for three days.