Situational

Opposite Lid

Keep an eye out for ways to create covers from the other side when you get pieces in a different order.
Covering with I can also be effective, but be wary when using L, J, or O; covering with these pieces can create unwanted hanging points or fill the space where you intend to form a hole.

Imperial Stairs

Look for this

Fill with S

In the case that you have an open imperial cross or T shape, fill it with S/Z finish a hole and start another.

Cover with Z

Build stairs with T

Cover holes with S/Z to create the foundation for new holes.

Place T next to this foundation to complete the hole and start a new one.

Hangs

Hanging points are structures that impede the direct creation of holes; pieces must instead be placed in so they are "hanging" from this structure in order to create a hole. Using O, L, or J to cover a hole have the highest potential for creating hanging points. A line clear may be necessary to continue, but sometimes "hanging" structures can be useful in quickly creating multiple holes with few pieces.
If the structure is 3 units tall, only L/J can be hung from the structure and complete a hole, making a line clear the best strategy.

If the structure is 2 units tall, all pieces but I can be hung from the structure to complete a hole. A few pieces will maintain the 2 unit structure, while a few will necessitate a line clear. T can successfully end the hanging structure without requiring a line clear.

In this diagram, O starts the structure and J and S maintain it. Z and L could have been used to end the structure by clearing a line, but T caps off the structure without a clear.