Technically, there's another option to save/retrieve chat logs besides Outlook. The parameter is called AutosaveChatsLocation. By default, this parameter should be enabled. After the user closes the conversation (chat) window, the chat log is saved under a local folder called MyJabberChats. You (Admins), or users can always change the folder path by going here;
Click on Jabber's Menu > File > Options > Chats and under Autosave Chats, verify the "Autosave chat sessions to..." checkbox has been checked. If needed, change the folder path. Admins can change the folder path globally via jabber-config file. Yes, I know. This doesn't address your 2nd question about accessing the chat logs from multiple devices.
With that being said, Jaime is completely right. If users want or need the ability to retrieve chat logs from any device, then your options would be Message Archiver (or) Third-Party Compliance Server. Cisco is pretty vague about which Third-Party Compliance Server (solutions) they support. They don't provide a list of pre-approved solutions. You need to reach out to Cisco, if you want to know. I assume... any Oracle-based, PostgreSQL-based or MS SQL-based Third-Party Compliance Servers (solutions) would be Ok.