Total number of four digit odd numbers that can be formed by using $0,1,2,3,5,7$, is

An odd number has an odd digit at unit's place. 

So, unit's place can be filled in 4 ways

Each of ten's and hundred's place can be filled in 6 ways. 

Thousand place can be filled in 5 ways

Hence, required number of numbers $= 5 x 6 x 6 x 4=720.$