IPA: //ˈstreɪtweɪ//
KK: /ˈstreɪtˌweɪ/
In a direct manner or without delay; immediately.
She went straightway to the store after work.
Straightway → It is formed from "straight" (from Old English *streht*, meaning direct or not bent) and "way" (from Old English *weg*, meaning path or road). The word "straightway" means directly or immediately along a path without deviation.
Think of a path that is 'direct' ('straight') and leads you 'along' ('way') — that's why straightway means to go directly or immediately.
No commonly confused words.