This is a significant upgrade path so there is really no "easy" way to do this. You cannot upgrade in place directly from Oracle 7 to 10gR2 so if you want to do the upgrade in one step, export and import is your best option. If you prefer to upgrade in place, according to the Oracle Database 10g Release 2 (10.2) Upgrade Guide, you will need to be at release 7.3.4, then you can upgrade to 126.96.36.199 and finally to Oracle 10gR2.
As mentioned, this is an enormous leap in database software technology so whatever option you choose, please ensure that you test the entire upgrade process from end to end in a non-production environment. There will likely be code changes to your applications, as well as some SQL tuning since the Oracle optimizer has changed dramatically from release 7.3.4 to 10.2. I'm assuming there is likely an operating system upgrade as part of this migration, too, so this will complicate the upgrade somewhat. If the database is not very large in physical size and you can take a reasonable outage to perform the upgrade, I would recommend using export and import. Export relevant schemas from the existing Oracle 7 database, and import them into the newly created Oracle 10gR2 database. You will still have to test thoroughly and likely make SQL and code changes, but at least this gets you to where you want to be in one big step, rather than two.
Dig Deeper on Oracle database export, import and migration
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