```ts
export function leagueOrder(matches: (string | number)[][]): string[] {
  // Validate matches
  for (const match of matches) {
    if (!Array.isArray(match) || match.length !== 4) {
      throw new Error("Invalid match format");
    }
    const [homeTeam, awayTeam, homeGoals, awayGoals] = match;
    if (typeof homeTeam !== "string" || typeof awayTeam !== "string") {
      throw new Error("Team names must be strings");
    }
    if (homeTeam === awayTeam) {
      throw new Error("A team cannot play against itself");
    }
    if (!Number.isInteger(homeGoals) || !Number.isInteger(awayGoals) || homeGoals < 0 || awayGoals < 0) {
      throw new Error("Goal figures must be non-negative integers");
    }
  }

  // Initialize standings
  const standings: { [key: string]: { points: number; goalDifference: number; goalsScored: number } } = {};

  // Calculate initial standings
  for (const match of matches) {
    const [homeTeam, awayTeam, homeGoals, awayGoals] = match;
    standings[homeTeam] = standings[homeTeam] || { points: 0, goalDifference: 0, goalsScored: 0 };
    standings[awayTeam] = standings[awayTeam] || { points: 0, goalDifference: 0, goalsScored: 0 };

    if (homeGoals > awayGoals) {
      standings[homeTeam].points += 3;
    } else if (homeGoals < awayGoals) {
      standings[awayTeam].points += 3;
    } else {
      standings[homeTeam].points += 1;
      standings[awayTeam].points += 1;
    }

    standings[homeTeam].goalDifference += homeGoals - awayGoals;
    standings[awayTeam].goalDifference -= homeGoals - awayGoals;
    standings[homeTeam].goalsScored += homeGoals;
    standings[awayTeam].goalsScored += awayGoals;
  }

  // Sort teams
  const sortedTeams = Object.keys(standings).sort((a, b) => {
    if (standings[b].points !== standings[a].points) {
      return standings[b].points - standings[a].points;
    }
    const headToHeadMatches = matches.filter(
      ([homeTeam, awayTeam]) => (homeTeam === a && awayTeam === b) || (homeTeam === b && awayTeam === a)
    );
    let headToHeadPointsA = 0;
    let headToHeadPointsB = 0;
    for (const [homeTeam, awayTeam, homeGoals, awayGoals] of headToHeadMatches) {
      if (homeTeam === a && awayTeam === b) {
        if (homeGoals > awayGoals) {
          headToHeadPointsA += 3;
        } else if (homeGoals < awayGoals) {
          headToHeadPointsB += 3;
        } else {
          headToHeadPointsA += 1;
          headToHeadPointsB += 1;
        }
      } else if (homeTeam === b && awayTeam === a) {
        if (homeGoals > awayGoals) {
          headToHeadPointsB += 3;
        } else if (homeGoals < awayGoals) {
          headToHeadPointsA += 3;
        } else {
          headToHeadPointsA += 1;
          headToHeadPointsB += 1;
        }
      }
    }
    if (headToHeadPointsB !== headToHead