manumahi,
Sad to hear about your loss.
The things you would probably need to do.
1. Get the photocopies of your GC filing so far from your lawyer. The lawyer's office will have all info of yours in their file (Better than employers).
2. Apply for passport at Indian embassy/consulate.
3. You should contact BCIS regarding EAD.
4. Check with SS if you would need to get a 'new' SSN.
5. Place a 'fraud alert' with the 3 credit reporting agencies. If anyone tries to apply for a credit card, etc. (anything that needs a credit check), the credit agencies will contact you before providing it to the banks, etc. You should also alert your bank to look for any suspicious transactions. Check these sites for any suggestions,
http://www.consumer.gov/idtheft/ ,
http://101-identitytheft.com/fraudalert.htm
6. If you have home/renters insurance, file claims with your insurance for the jewelry.
7. Using degree copies, etc. from your lawyer, ask family/friends to check college, etc. for obtaining new degree certificates.
8. Check with your landlord as to who have access to your apt.
In the future,
1. Have a bank locker (chances of robbery is lesser compared to an apt/house). Have a set of all important docs (possibly originals) at bank and copies at home. A good size locker will cost <$100/yr mostly.
2. Try buying renter's insurance. Notify insurer of the jewelry/valuables in house/bank locker (bank does not cover it if lockers are robbed). Can get coverage for about $25-50K for about $100-250/yr.
3. Unless you can't avoid basement/first floor apartments because of kids, etc., the second floor and above are in general considered a bit more safer.
Hope your situation will be rectified soon. Good Luck.
p.s.: I have heard cases where Indian households are targeted for burglary because of the jewelry that we carry. The immigration docs, etc. were possibly stolen because they were along with the jewelry in the same box, etc.