Odd divisor summation
First I would suggest to separate the code into two functions: One which computes the sum of odd divisors of a single number, and another which adds the odd divisors of all numbers in a list. Also, use better function names, and add at least a simple doc comment:

def oddDivisorSum(n):
    """Return the sum of odd divisors of n."""
    # ... to do ...


def totalOddDivisorSum(numbers):
    """Return the sum of all odd divisors of all numbers."""
    return sum(oddDivisorSum(n) for n in numbers)


This makes the code more clear, better reusable, and makes it easier to add test cases.

To make the computation faster, two observations help:


If \$k\$  is a divisor of \$n\$, then \$\frac{n}{k}\$ is also a divisor of  \$n\$.

This is what Oscar also said, and it allows to restrict the search for divisors to the interval  \$1\dots \sqrt n\$. The "problem" is that \$k\$ and \$\frac{n}{k}\$ can have different oddity.
If \$ k \$ is an odd divisor of an even number \$n\$ then \$k\$  is also an odd divisor of \$\frac{n}{2}\$.


Therefore, we can remove all even factors of \$n\$ first, and then find odd divisors in the reduced (odd) number. This makes the code simpler (because all divisors are odd) and faster for even numbers (a smaller \$n\$ means less trial divisions):

def oddDivisorSum(n):
    """Return the sum of odd divisors of n."""
    while n % 2 == 0:
        n //= 2
    sum = 0
    for k in range(1, int(n ** .5) + 1, 2):
        if n % k == 0:
            sum += k
            if n // k != k:
                sum += n // k
    return sum