Operational decision

Answer: $\times$

Guessing

$3\div4$ is not a whole number so it's probably not $\div$

$1\times2\times(3-4+5)\times(6\times7+8+9)=2\times4\times59=8\times59\approx240$ too small

$1\times2\times(3+4+5)\times(6\times7+8+9)=2\times11\times59=22\times59\approx 1200$ too small

$1\times2\times(3\times4+5)\times(6\times7+8+9)=2\times17\times59=34\times59\approx 2100$ about right

So it must be $\times$

Working backwards

From the original equation

$$1\times 2\times (3\oplus 4+5)\times (6\times 7+8+9)=2006$$it follows that

$$2\times (3\oplus 4+5)\times (6\times 7+8+9)=2006,$$that is $\left(3\oplus 4 + 5\right)\times 59 = 1003$, that is $3\oplus 4 + 5=17$, that is $3\oplus 4=12$. Therefore, $\oplus$ should be replaced by $\times$.