I can think of a couple that would work.
Like 99. 9+9=18 (multiple of 9), it's odd and has two digits.
.
The full set is 27 45 63 81 99.
45
2: The number ends in 0, 2, 4, 6 or 8 4 : The last 2 digits are a multiple of 4 The 10s digit is even and the last digit is 0, 4 or 8 The 10s digit is odd and the last digit is 2 or 6 8: The last 3 digits are a multiple of 8 The 100s digit is even and the last 2 digits are a multiple of 8 The 100s digit is odd and the last 2 digits are 4 times an odd number 16: The last 4 digits are a multiple of 16 The 1,000s digit is even and the last 3 digits are a multiple of 16 The 1,000s digit is odd and the last 3 digits are 8 times an odd number 32: The last 5 digits are a multiple of 32 The 10,000s digit is even and the last 4 digits are a multiple of 32 The 10,000s digit is odd and the last 4 digits are 16 times an odd number 64: The last 6 digits are a multiple of 64 The 100,000s digit is even and the last 5 digits are a multiple of 64 The 100,000s digit is odd and the last 5 digits are 32 times an odd number 128: The last 7 digits are a multiple of 128 The 1,000,000s digit is even and the last 6 digits are a multiple of 128 The 1,000,000s digit is odd and the last 6 digits are 64 times an odd number 256: The last 8 digits are a multiple of 256 The 10,000,000s digit is even and the last 7 digits are a multiple of 256 The 10,000,000s digit is odd and the last 7 digits are 128 times an odd number 512: The last 9 digits are a multiple of 512 The 100,000,000s digit is even and the last 8 digits are a multiple of 512 The 100,000,000s digit is odd and the last 8 digits are 256 times an odd number 1,024: The last 10 digits are a multiple of 1,024 The 1,000,000,000s digit is even and the last 9 digits are a multiple of 1,024 The 1,000,000,000s digit is odd and the last 9 digits are 512 times an odd number
The number 1111115
The last 3 digits are a multiple of 8:The 100s digit is even and the last 2 digits are a multiple of 8The 100s digit is odd and the last 2 digits are 4 times an odd number
The last 5 digits are a multiple of 32The 10,000s digit is even and the last 4 digits are a multiple of 32The 10,000s digit is odd and the last 4 digits are 16 times an odd number
The last 4 digits are a multiple of 80The 1,000s digit is even and the last 3 digits are a multiple of 80The 1,000s digit is odd and the last 3 digits are 40 times an odd number
No. A multiple of an even number cannot be odd.
There are 5760 such numbers.
odd - even numbers are a multiple of 2.
Temporary lodging
A number is a multiple of 16 is the last 4 digits are a multiple of 16 The 1,000s digit is even and the last 3 digits are a multiple of 16 The 1,000s digit is odd and the last 3 digits are 8 times an odd number
21 or 35