I've been trying to solve same problem with python and I think I've figured out a way that covers all the cases that are possible given the mathematical definition of an odd number. I've tested it and it works, I wonder what do you think.
counter = 0
odd = []
even = []
while counter < 10:
x = int(input("Enter a number: "))
if abs(x)%2 == 0 and x != 0:
even.append(x)
else:
odd.append(x)
counter += 1
if len(odd) == 0:
print("No odd number was entered")
else:
print("The largest odd number is:", max(odd))