Muscle
Fibrosis
Overuse causing trauma on a microscopic level can lead to damage of muscle fibres. The repitive trauma promotes the formation of adhesion's within the muscle. These adhesion's can inhibit the muscles ability to contract and relax and damage muscle or tendon around the site of injury.

Ligament
Over use injuries are uncommon for ligaments. Ligaments are more susceptible to acute injuries.

Tendon

Overuse injuries are most commonly found in Tendons. Tendons are able to withstand large forces due to the tight parallel collagen bundles. Tendons have the ability to slightly stretch before failure, although as tendons are repetitively loaded and stretched into a length where microscopic tears occur, the parrallel collagen fibres are separated and damaged. 

Bone
Stress Fracture
Stress fractures are common in sports people, people who undertake repetitive tasks (sport or work) and the elderly who have osteoporosis. Stress fractures can occur due to 2 main mechanisms:
Increased and repetitive force over a particular area of bone

The force of muscles repetitively pulling on their boney attachments

It is important to note that X-ray will generally be clear, Bone scan, CT or MRI are more commonly used for diagnosis.

Periostitis

The periostium is the outer layer of the bone and can be damaged from tendon's pulling on the boney attachment. This commonly occurs on the Tibia bone and is colloquially known as 'shin splints'.

References:

Bruckner, P & Khan, K 2006, Clinical Sports Medicine, 3rd edn, McGraw-Hill, North Ryde, NSW.
Image: https://www.scientificanimations.com/wiki-images/

Tips
When dealing with an overuse type of injury, it is important to get to the specific cause of the issue rather than solely focusing on the localised treatment of the painful area of the body. Finding the cause of the problem and treating it will help prevent an overuse injury from reoccurring.