Well, seem like not many people aware that Civil/Structural Engineer can really work in Oil and Gas industry. Actually to work in oil and gas as structural engineers, you can become consultant, contractors, service engineers or working for client company.
For Consultant you can apply for,
Technip, Ranhill WorleyParsons, RNZ, MMC Oil Corp, Noble Denton, Germanischer Lloyd (Malaysia), APL, etc...
For Contractors (fabricating the structures),
Kencana HL, MMHE, Ramunia, Brooke Dock Yard, Sime Engineering Yard
For Service Engineers,
Aker Kvaerner, Single Buoy, J. RAY MCDERMOTT (normally prefer experienced engineer), Sapura Crest, etc...
For Client Engineer, you can apply for
Shell, Petronas, Talisman*, Murphy*, ExxonMobil* (* tend want experience structural engineer but can try)
For doing not related to structure, with high pay and long working hours, you can try to apply schlumberger.
There are more actually but this is what i can think of for now.
Btw I am structural engineer working in one of the consultant for less than a year (just graduated last year).
Just to add, Single Buoy Moorings (SBM) and Aker Kvaerner are consultants also.