------
## 最终结论
```python
def double_the_difference(lst):
    if not lst:  # 处理空列表情况
        return 0
    
    # 过滤有效数字：筛选出正整数并且是奇数的数字
    odd_numbers = [num for num in lst if isinstance(num, int) and num > 0 and num % 2 != 0]
    
    # 计算平方和
    sum_of_squares = sum(num ** 2 for num in odd_numbers)
    
    return sum_of_squares

# 测试用例
print(double_the_difference([1, 3, 2, 0]))  # 输出: 10
print(double_the_difference([-1, -2, 0]))    # 输出: 0
print(double_the_difference([9, -2]))        # 输出: 81
print(double_the_difference([0]))             # 输出: 0  
print(double_the_difference([]))              # 输出: 0
```