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WebSphere Profiles:

For migrating WebSphere Application Server (WAS) itself (and its configuration), all the tools that you need already come with WAS V8.5.x.

You would use WASPreUpgrade and WASPostUpgrade to migrate your WebSphere Profiles or you can opt to use the Migration Wizard graphical interface to those tools to help facilitate and automate the task for you.

Migrating product configurations with migration tools

https://www.ibm.com/docs/en/was-nd/8.5.5?topic=configurations-migrating-product-migration-tools

https://www.ibm.com/docs/en/was-nd/9.0.5?topic=configurations-using-migration-tools

Migrating profiles using the migration wizard

https://www.ibm.com/docs/en/was-nd/8.5.5?topic=configurations-migrating-profiles-using-migration-wizard

https://www.ibm.com/docs/en/was-nd/9.0.5?topic=tools-migrating-profiles-by-using-migration-wizard

Applications:

There is also a handy Migration Toolkit available that can be very helpful to migrate your Applications from previous WebSphere 7.x or 8.x to 8.5.5 full profile or Liberty, and also from other 3rd party application servers such as JBoss, Tomcat, Weblogic and so forth.  There is also a WebSphere Configuration Comparison Tool that can help facilitate the task.

For more information see:

WebSphere Application Server Migration Toolkit

https://www.ibm.com/support/pages/websphere-application-server-migration-toolkit

WebSphere Application Server Configuration Comparison Tool

https://www.ibm.com/support/pages/websphere-application-server-configuration-comparison-tool

Java 8:

Now, regarding switching WebSphere to point to the newer Java 8 from previous or default Java 6 or Java 7, you can use the manageSDK command to accomplish this task.

managesdk command

https://www.ibm.com/docs/en/was-nd/8.5.5?topic=tools-managesdk-command

https://www.ibm.com/docs/en/was/9.0.5?topic=tools-managesdk-command