Ignoring the honourable mentions because the list would be too long, my top picks for each category are:
GK - Schmeichel, and it is not even close.
Defender - purely on performance, I would rank Vidic above Kompany, but the latter's inspiring leadership and influence in helping City become the top team in the league in over the last few years cannot be understated, which is why I would go with him.
Midfielder/Winger - It is difficult to look beyond the trio of Ronaldo, Vieira and Silva. Purely as an individual player, Ronaldo is head and shoulders above the rest and inarguably the second greatest player of the modern era, but we didn't see his best in the Premier League. He took his game to the next level in 2007-2008, but he left for Madrid in 2009. Had he stayed in Man United for another two seasons, this wouldn't even be a debate.
Vieira, along with Kompany and Keane, is probably the greatest captain the PL has seen. He wasn't the flashiest player in the invincible squad, but he was the one who brought that winning mentality and aggression to the team. His departure in 2005 signalled a decline for Arsenal that they are yet to recover from, and he is yet to be replaced in 14 years.
Silva is one of the greatest technicians to have ever played in the league. He is no Xavi or Iniesta, but he is still one of the greatest Spanish midfielders of all time. Along with Kompany and Aguero, he has been the most important driving force behind the success of Man City in this decade. This is a tough call for me, but I would just about go with Vieira.
Striker - probably the most competitive category. The PL has been blessed with some phenomenal strikers who have elevated the standard of the league. Before the emergence of Ronaldo, Henry was the hottest overseas superstar in the Premier League, and a player who was feared by each and every team and manager in the country.
He was the king of England for years and no one could touch him. A shame that his last season was marred by injuries and his heart was never at Arsenal after the fateful night in Paris in 2006. He was a big factor in making Premier League the most popular league in the world and even rival fans had noting but admiration for him.
Aguero - apart from producing the greatest moment in history of English football, he has been world class in every season and has been a symbol of consistency. He has been able to adapt his style to different managers without impacting his scoring rate.There is no question that he is the best foreign player of the decade, but I can't put him above someone like Henry who was clearly the superior individual player and also had longevity.
Suarez - In terms of individual ability, he is arguably the best forward to have played in England, and I would actually rank him above Henry. He was simply outrageous in 2013-2014 and even better than Henry in 2003-2004. However, he simply didn't spend enough time in England to be ranked above Henry and even Aguero, who is not as good as him but his longevity and influence cannot be ignored.
Van Nistelrooy - The greatest fox in the box/poacher to ever play in the league. A deadly finisher who carried Man United's attack before the emergence of Ronaldo and Rooney, but his limitations as an all-round player made him surplus to requirement are 2006. SAF's decision to sell him in 2006 improved the fluidity of Man United's attack and helped them restore their dominance in the league.
It is hard to pick between Henry, Aguero and Suarez - in terms of individual ability, Suarez beats Henry by a nose but he had no longevity. Hence, I would go with Henry because he was not only a better player than Aguero, he also had the longevity unlike Suarez.
Overall, my pick for the best foreign player in the Premier League would be Henry.