Wordnet 3.0
ADVERB (2)
1. 
 at once; 
- Example: "straightway the clouds began to scatter"2. 
 in a direct course; 
- Example: "plunged straightway to the rocks below"
The Collaborative International Dictionary of English v.0.48:
Straightway \Straight"way`\, adv.
   Immediately; without loss of time; without delay.
   [1913 Webster]
         He took the damsel by the hand, and said unto her,
         Talitha cumi. . . . And straightway the damsel arose.
                                                  --Mark v.
                                                  41,42.
   [1913 Webster]
WordNet (r) 3.0 (2006):
straightway
    adv 1: at once; "straightway the clouds began to scatter"
    2: in a direct course; "plunged straightway to the rocks below"