Lyophilized powders should be frozen & will maintain efficacy for a period of time measured in decades. If it's a modern fridge/freezer combo or most modern chest/upright freezers, you can use something like an insulated Hydrapeak Food Jar to help maintain consistent temps through the regular automatic thawing cycles to prevent frost. If your plan is to use them within a couple years or so though this is probably an unnecessary step but you can get some inexpensive inserts made from silicone (or 3D print them) specifically for 3mL (or 5/10mL) that helps with organization if that's something you're into.
If reconstituted, refrigerator only to help slow the growth of bacteria. Don't freeze. The official stance by USP for reconstituted peptides is 28 days but many are okay with 2-3 months with a handful of crazy MFers willing to extend it much further in some cases. Comes down to personal comfort level w/risk beyond the official 28 day guideline. Personally, I'll go 2mos comfortably but beyond that I'm doing some back-of-the-napkin math on how much $ I'd be out if I dumped it. More often than not my health isn't worth that amount of financial loss. Especially when you factor in a trip to the ER these days. Kind of blows up the budget to save tens of dollars.
If we're talking oils you're good at room temperature for quite a while since oil doesn't allow bacteria growth the same way water based solutions (like peptides) can.