Thanks for the extra information. It looks like day and night temperatures are now just about warm enough where you are, but they may not have been when you planted them out. It also sounds like you did not harden them off before planting outdoors - the plant store you bought them from will either have had them under shelter day and night, or brought them under shelter at the end of the working day, so they would have needed hardening off. Coleus grow best in warm soil and air temperatures over 60degF, so if the temperature of either soil or air, particularly overnight, was low, this would explain why they look droopy like this. Note that Coleus do not really appreciate full sun, they prefer dappled shade or full sun restricted to early mornings or late afternoons only.
Now that temperatures are warming up, they should hopefully recover and start to grow on.