There are 15 different modes, but you can do anything in party mode. Sorry I can't give you details about game invites (though people playing offline receive a text) as I haven't really got into playing online

 In all PS3 games users used PSN ID (only MGO have konami id). In GTA player who creat game can change game mode, weapons, auto-aim off/on and more. But most important thing is player can set up private slots so we can play clan wars. 

 What modes are there? What mode should such a league have, is there a more common mode? Is GTA 4 teamplay (that would discalify it somehow) everybody against everybody?

GTA IV also has several co-op modes which are meant to be good, though I have not played any of them yet

Deathmatch and Race sounds intresting, what do you guys want first? All those modes can be done in private (only VGC members)? And other can find this private thing by the live ID of the hoster?

 You must have people in psn list to join their serwer (room). Game don't have serwer search. All modes can be done in private.  

How GTA multiplayer works: a player (host) uses his in-game cell phone to launch a party. The party is essentially the game world, complete with pedestrians, cars and weapons. He then starts sending invites to his friends who will appear in the game world and be able to interact with it (pedestrians, cars, weapons) and other players. This mode can go on forever, but there is no score that is kept tracked of.

The host can then use his cell phone to bring all the players in the party into one of the game modes below taken from Wikipedia. In my brief experience being host, when you select a game mode, it sends you into an existing game (with strangers). There may be a way to stay as a closed party games, but in my brief experimentation, I have not found the option.

Most of the interesting modes are team based, except for deathmatch and races. After a game, you do get a read-out of people's kill/death ratio, so that could be tracked. You also get money for each mode. Maybe money would be the best way to track the league, assuming it is based on performance and not participation.

EDITED TO ANSWER ONE OF Just_Ben's questions: You have to receive an invite from a VGC leaguer. Unlike warhawk, you cannot search and join one of your friends without him sending you an invite. Which means participants MUST have other participants on their PSN friends list.

From wikipedia:

Multiplayer

Grand Theft Auto IV is the first console game in the series to include online multiplayer, with 15 modes of play available.[32] The multiplayer supports up to 16 players and allows players to explore the entire city.[33] Players use a customisable character in a majority of the modes, with cash earned during play able to be used to purchase clothing for their character. Hosts of the games can control many variables, such as time of day, police presence, pedestrian presence, traffic, location of game, and weapons. The online games are split into ranked and unranked matches. The reward for the ranked gameplay is cash, which determines players' ranks.[34] The game does not feature any split screen or LAN multiplayer modes.[35]

There are several different game modes available. Team based gameplay modes include[20] Team Deathmatch, where 2-8 teams compete to accumulate the most kills in a traditional deathmatch; Team Mafiya Work, in which 2–8 teams compete to complete contract work for the "mafiya", such as escorting/killing targets or stealing cars; Team Car Jack City where 2–8 teams compete to steal cars and earn money for keeping them undamaged; Cops n' Crooks, featuring a team of cops who must compete against a team of crooks (which features the "All for One" variation - requiring the cops to kill the crooks' "Boss" before he is escorted to the extraction point - and the "One for All" variation - requiring the cops to kill all of the crooks before they reach the extraction point); and Turf War, involving two teams who compete to take control of designated areas of the map and control them for as long as possible.

The game also includes a variety of racing and co-operative modes, which include Race, in which players race through checkpoints in a traditional automobile race; a GTA Race variation, where players race through checkpoints in an automobile race, with the ability to combat their opponents; Hangman's N.O.O.S.E., a co-op mode that requires players to collect a person from the airport and safely escort him to the extraction point before the cops kill him; Deal Breaker, a co-op mission that requires players to assault a construction site captured by enemies, then chase a group of enemies before they escape; and Bomb da Base II, a co-op mission that requires players to clear out a ship, then destroy it with explosives. The game also features a Free Mode, in which players have the entire map open to explore, with no end goal or mission to complete.

 And with a certain ranking after an given time, shown to everybody (for races the place, for death match, kills or money or what ever is the goal in death match.

 When times up score table is show for everybody. But when you want look for your score when you play you must press d-pad (down button).