The 63 individuals are due to go to trial in Texas in August, suing for millions of dollars. If they ignore the injunctions they would be in contempt of court and liable to be jailed, the OILC said.
The families and survivors were told of the injunctions in a letter from the oil companies involved, including Exxon Corporation, Shell UK Ltd, Shell Exploration UK Ltd and Esso Exploration and Production UK Limited.
If the action for damages were confined to the UK courts, any compensation awarded would be in the hundreds of thousands, compared with the millions that could be awarded in the US. The families' legal team is believed to be taking action to counter the injunctions.
A spokesman for Shell said it was thought 'appropriate that the matter should be resolved in Scotland'.