Safely thaw and refreeze sorbet

Almost any normal sorbet recipe will contain a decent amount of sugar, and strawberries are no exception. I'd guess probably 1/2-2/3 cup per pound of strawberries. Use a substitute if you have an aversion - honey, agave, raw cane sugar, whatever you prefer. (Of course, anything liquid is going to contain some water, and cause a bit of ice, but it's still doable.) A sorbet without any extra sugar, even when frozen normally in an ice cream maker, is going to end up with a very icy texture, which will probably keep you from experiencing the flavor as much. The sugar helps soften it.

The other common way to soften a sorbet is alcohol. Rosé wine (thank you, David Lebovitz) works quite well in a strawberry sorbet. Vodka can be your go-to liquor for any impromptu sorbet with other fruits, since it'll add alcohol without any flavors that clash. Beyond that, either look for recipes, or look for mixed drinks containing the fruit you're using.

You might also be having problems simply because your strawberries aren't that great. Did you freeze them, or were they storebought? If you bought the strawberries yourself, you'd know they were decent before freezing, while not all storebought frozen fruit is as flavorful.

Finally, it's possible that your frozen strawberries collected some extra water in the form of frost, which then makes your sorbet icier. If there are obvious big chunks you could scrape them off.

The general things that can cause icy sorbet:

• Too much water Compared to other ingredients. Since you probably aren't going to take water out of your fruit, you pretty much have to add sugar or alcohol to compensate for this. This is tricky if you're improvising, and if the water content of the fruit varies.
• Bad churning/freezing: This is mostly determined by the ice cream maker you have. It sounds like you're probably okay, since you get good results sometimes, but if the churning isn't good, you can get big ice crystals as it freezes around the outside before getting mixed well. If you're using the common type with a pre-frozen vessel, make sure you've frozen it thoroughly, so that you can churn long enough to smooth things out.
• Chunky fruit: Big chunks will be really obvious, but even tiny chunks can help provide little bits that make the result freeze hard. Make sure that you puree well.
• Too cold a freezer: sorbet is going to be best if it's not frozen extremely cold, but your freezer probably is nice and cold. Be willing to let it sit out a little bit before eating, or and perhaps keep it in the door where it's slightly warmer.

David Lebovitz has a good blog post about making homemade ice cream softer; most of what I've mentioned is also there, along with more details and some things that apply only to ice cream - for example, fat softens things too.