There are a lot of ways to do this. If you want a command line fast solution, this one can deal with your issue:
awk 'BEGIN{RS = ">" ; ORS = ""}NR==2{ min=length($2); max=length($2); next} max < length($2) {max=length($2)} min > length($2) {min=length($2)} END {print "Shortest: "min"\nLongest: " max"\n"}' file
Basically you need to extract the length of each sequence, and save the highest and lowest value. As I told you, there are a plenty ways to do it, in different languages, or different tools. In my opinion awk is great for this kind of situations.