To find the number of 3-digit numbers between 100 and 999 inclusive, we need to consider the following conditions:
1. The number should have only odd digits occupying odd places.

Let's break down the problem into smaller steps to find the solution.

Step 1: Odd digits occupying odd places
Odd digits are 1, 3, 5, 7, and 9. Since the number should have only odd digits occupying odd places, the possibilities for the hundreds place, tens place, and ones place are as follows:
- Hundreds place: 1, 3, 5, 7, or 9
- Tens place: 1, 3, 5, 7, or 9
- Ones place: 1, 3, 5, 7, or 9

Step 2: Counting the possibilities
To find the total number of possibilities, we need to multiply the number of choices for each place.

- Hundreds place: There are 5 possible choices (1, 3, 5, 7, or 9).
- Tens place: There are 5 possible choices (1, 3, 5, 7, or 9).
- Ones place: There are 5 possible choices (1, 3, 5, 7, or 9).

Therefore, the total number of possibilities is 5 * 5 * 5 = 125.

Step 3: Excluding numbers less than 100
Since we need to find the numbers between 100 and 999 inclusive, we need to exclude numbers less than 100. There are 9 numbers less than 100 (1-digit numbers from 1 to 9).

Step 4: Final calculation
To find the final answer, we subtract the excluded numbers from the total number of possibilities.

Final answer = Total possibilities - Excluded numbers
= 125 - 9
= 116

Therefore, the correct answer is option D) 116.