Liverpool midfielder Gerrard was restricted to light work during England’s first training session in Brazil on Monday and was believed to be struggling with a groin problem.
But, addressing the media for the first time in Rio de Janeiro, Hodgson insisted he is cleared to play against Italy in their Group D opener on Saturday.
"We did a training session yesterday where the players who didn't play on Saturday against Honduras trained, and some of the others did a warm-down session," he said.
"Steven did some extra work at the end of that training session. There's nothing wrong with him and I don't understand that story at all."
Arsenal’s Oxlade-Chamberlain suffered a knee injury in the warm-up game against Ecuador last week.
Hodgson has been pleased with the 20-year-old's progress but stopped short of suggesting he would recover in time to feature against the Italians.
"He's done very well and will work on his training programme during the course of the week,” he said.
“But it’s a job for me to say when he will be ready. It’s a medical matter. There are no guarantees. The medics are hoping he could be fit by the second game."
England have no other injury concerns as they prepare for the game in Manaus and Hodgson is happy he has a wealth of quality players to choose from.
"It's good to have selection issues," the 66-year-old said. "It's good to have choices and have different people selecting different teams.
"It shows we've got enough players that people believe are good enough to play for their country."
Hodgson, meanwhile, is convinced that England are better suited to contain Andrea Pirlo this time than they did at Euro 2012.
England slipped out of the European Championships on penalties following a goalless draw at the quarter-final stage - a game in which Pirlo pulled the strings throughout before converting a remarkably composed Panenka-style spot-kick in the penalty shoot-out.
He said: “How are we going to stop Pirlo? What we’re going to do first of all is we’re going to play better against Italy this time than we did in Euro 2012.
“Of course, against a tiring team and a team that was playing with Pirlo, he had a very, very good game because he’s a very, very good player.
“What are we going to do this time against Pirlo? First, we’ll play with more energy because we’ll have more energy because it will be the first game in the tournament. We’ll be even more compact than we were in that game."
Brazil legend Pele expects Hodgson's troops to progress past the group stages while insisting Wayne Rooney would start in any team of his.
Manchester United striker Rooney has failed to score in eight appearances at the World Cup finals and there have been calls for Hodgson to leave him out of the starting line-up.
However, Pele expects Rooney to play a key role and help England reach the knockout stages of the tournament by qualifying from Group D which also contains Italy, Uruguay and Costa Rica.
The 73-year-old, who won the World Cup three times with Brazil, told Sky Sports News: “It is a difficult group but I think England could pass.
“Of course today it is very, very even; the majority of the players play in Europe, like Brazil. Brazil have 11 players playing in Europe. England have a difficult group but I think they could pass.
“The World Cup is a very short tournament and the experienced players always do well.
“Wayne Rooney has not scored [in a World Cup final stage] but he was fantastic for the team. He was always the player who fought more for the team – I would like him in my team, you know!”