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Going to your first question on whether you need to run IRM, answer is yes, IRM is mandatory if you are patching Siebel application from 8.1.1.x to 22.214.171.124. Its irrespective of if you are using OpenUI or not.
Coming to installation, you need to download 126.96.36.199 jar files, you can follow below steps to download same. Then create image and apply patch.
1) Login to My oracle support through your credentials
2) Go to tab 'Patches & Updates'
3) Enter patch number as '17470764' in 'Patch Name or Number' field and click on search.
4) Download patch for AIX.
You can get really helpful information on installation and other post installation tasks in following knowledge documents:
Innovation Pack 2013: Installation instructions for Siebel 188.8.131.52/184.108.40.206 (Doc ID 1590380.1)
Install & Configure Advisor: Siebel Innovation Pack 2013 (220.127.116.11/18.104.22.168) (Doc ID 1588620.1)
I hope it helps.