If a person replaces the straps of Tefillin with new ones, can the old ones be stored in the same pouch as the Tefillin?
Yes, it may be used for tefillin straps.
See Pri Megadim O:C 153:15 and MIshna Brura 154:6 who rule that something which services “tashmishei kdusha”, things which themselves are servicing articles of kedusha, itsleh has no kedusha and may be used for non kadosh items. A tefillin pouch which holds tefillin which are themselves in another casing, would be an example of this halacha. As such they may be used for any purpose as long as it is not disgraceful to the tefillin.
cf. Daas Torah in the above siman who is more stringent and rules that as long as it is still serviciing the holy objects, it should be used for non holy objects.