1-digit: $1, 3, 7, 9$ (excluding 0) $= 4$

2-digit: First digit: 4 choices (1,3,7,9); second: 5 choices $= 4 \times 5 = 20$

3-digit: First digit: 4 choices; others: 5 each $= 4 \times 5 \times 5 = 100$

4-digit $< 7000$: First digit must be $1$ or $3$ (2 choices, since 7000 and above excluded — first digit can be 1, 3 only for $< 7000$; digits 7 and 9 give $\geq 7000$): $2 \times 5 \times 5 \times 5 = 250$

Total $= 4 + 20 + 100 + 250 = \mathbf{374}$