Number of odd integers between 1000 and 8000 which have none of their digits repeated is

1. For a number to be odd the digit in  units place should be 1,3,5,7,9

case(1)

Let the units  place is filled with 9

Since the required number is less than 8000

first place canot be filled with o,8,9.

So thousands place can be filled using digits from 1 to 7

and remaining two places can be filled in 8.7 ways
Then we have 7.8.7=392 

case (2)
If the units place is filled using 1,3,5,7 then

thousands place can be filled in 6 ways

middle two places in 8.7 ways
We have $\left(6\right)\left(8\right)\left(7\right)\left(4\right)=1344, (0,9(\text{ or }\left)8\right)$can not come at thousands place.
Total $392+1344=1736$ .