```python
from typing import List

def league_order(matches: List[List]) -> List[str]:
    if any(len(match) != 4 for match in matches):
        raise ValueError("Each match must be a 4-item list.")
    
    if any(not isinstance(item, (int, str)) or item < 0 for match in matches for item in match if isinstance(item, int)):
        raise ValueError("Invalid goal figure or team name.")
    
    if any(match[0] == match[1] for match in matches):
        raise ValueError("A team cannot face itself.")
    
    teams = set()
    for match in matches:
        teams.update(match[:2])
    
    standings = {team: {"points": 0, "gd": 0, "gs": 0} for team in teams}
    
    for home, away, home_goals, away_goals in matches:
        standings[home]["gs"] += home_goals
        standings[away]["gs"] += away_goals
        
        if home_goals == away_goals:
            standings[home]["points"] += 1
            standings[away]["points"] += 1
        elif home_goals > away_goals:
            standings[home]["points"] += 3
        else:
            standings[away]["points"] += 3
        
        standings[home]["gd"] += home_goals - away_goals
        standings[away]["gd"] -= home_goals - away_goals
    
    sorted_standings = sorted(
        teams,
        key=lambda team: (
            standings[team]["points"],
            standings[team]["gd"],
            standings[team]["gs"],
            team
        ),
        reverse=True
    )
    
    return sorted_standings
```