I want to translate my plugin for non-English languages. But for readme strings, I could find the only option to submit translations over translate.wordpress.org. Is there any way like the one available for plugin strings where you can ship plugin strings with the release without waiting for your translations to get accepted?
You can ship translations of some of the metadata used in your main plugin file's header comment fields. Namely:
Just add the source strings into your PO/POT files exactly as they appear in your plugin headers. When a MO file is available containing these strings, WordPress will display the translations on the plugin activation/listing screens.
e.g. POT entry:
#. Name of the plugin msgid "My Awesome plugin" msgstr ""
If you want to translate the entire readme.txt file, then as already mentioned in the comments - you can't. That file is only translated on wordpress.org when localised by the Glotpress team.
Note that the modal/popup that opens from the "View details" link on the plugins page is hosted on wordpress.org, so the latter applies.