Use all the digits 9, 2, 0, 3 to form

1. Determine the condition for the number to be odd

For the number to be odd, the last digit must be odd. The available odd digits are $3$ and $9$.

2. Determine the arrangement for the greatest possible number

To make the number as large as possible, the largest available digit should be placed in the highest place value (thousands). Thus, the first digit must be $9$. This leaves $3$ as the only available odd digit for the last position (ones).

3. Arrange the remaining digits to maximize the number

The remaining digits are $2$ and $0$. To maximize the number, place the larger digit ($2$) in the hundreds place and the smaller digit ($0$) in the tens place. The number is $9203$.

1. Find the smallest possible number starting with 3

Using the digits 9, 2, 0, 3, the smallest number starting with 3 is $3029$. The difference from $3000$ is $3029 - 3000 = 29$.

2. Find the largest possible number starting with 2

The largest number starting with 2 is $2930$. The difference from $3000$ is $3000 - 2930 = 70$.

3. Compare the differences to find the closest number

Since $29 < 70$, $3029$ is closer to $3000$.