Avian parasites consist of Protozoa, Worms and Mites. The result of the infection depends on the acuteness of infection. The most common cause for such infection in birds in aviaries is due to lack of proper quarantine. Birds kept in outdoor aviaries and new imports are susceptible to this infections. 
How to detect the infection
1. Examining the feces visually.
2. Taking a swap of the vent, or any lesion in the body for clinical investigation
3. Flotation is done by mixing feces in a solution which will cause parasite eggs to float to the surface and it is then examined under microscope for evaluation. 
Types of Protozoa 
This gastrointestinal parasite does not require an intermediate host. It is passed by ingestion of contaminated food and water. Parents can pass it to young during feeding. This infection is very common in finches causing loss of voice. I have found that this has been cause of dead young nestlings dead in nest. Due to loss of voice they do not beg for food and are not feed, hence die of starvation. Signs of this infection in adult bird are loss of weight, difficulty in breathing. This infection is also found in Amazons, Cockatiels, Budgerigars apart from finches were it is very common. 
Medication : Ronidazole, Metronidazole.
Brand name : Ronivet (Aus), Flagyl, Normetrogyl, Ivipet plus. 
Transmission is due to ingestion of food contaminated with feces from infected birds. Cysts are stable in the environment and serve as a source of infection. Hence it is very import that the cages and aviaries should be kept in hygienic condition by cleaning them regularly to avoid any infection from contaminated droppings Very commonly infects Budgerigars, Cockatiels, Lovebirds and Gray cheeked parrot. But it is rarely seen in South American parrots and Cockatoos and has not been reported Finches or Canaries. Signs of this infection are mucous diarrhea, loss of appetite, weakness, and recurrent yeast infection, High mortality in the nest, stunt growth common in case of neonatal Budgerigars and Cockatiels. Feather picking is a clinical manifestation, especially in Cockatiels and IRN. 
Treatment - Metronidazole. 
Brand name : Flagyl, Normetrogyl
Common found among Cockatiels and Lories. Similar to Giardia causes loss of weight or diarrhea 
Treatment is similar to Giardia.
Brand name : Flagyl, Normetrogyl
Commonly found in Canaries, Finches, and Lories. Infections in mynahs and toucans rarely clinical unless stressed in crowded unsanitary conditions. Diagnosis is through direct fecal or flotation. 
Treatment - Metronidazole.
Brand name : Flagyl, Metrogyl.
Blood Parasites 
It is a commonly occurring avian blood parasite, especially in wild caught Cockatoos. Up to 50% of wild caught imported were found to be positive, while only 5% of long term captive birds were positive. Clinical signs, if they occur, can rangr from enlarged spleen, enlarged liver and fluid in lungs it is a commonly occurring avian blood parasite, especially in wild caught Cockatoos. Up to 50% of wild caught imported were found to be positive, while only 5% of long term captive birds were positive. Clinical signs, if they occur, can range from enlarged spleen, enlarged liver and fluid in lungs. Diagnosis is done by taking a peripheral blood smear to identify gametocytes which encircle RBC nucleus. A bird can be the asymptomatic but when its immune system is down or stressed bird It can cause serious problem due to high level parasites in blood . 
Treatment - not recommended in asymptomatic birds, if affected and showing signs of infection -Quinacrine.
Types of Worms
Birds can be infected but still remain asymptomatic. Most commonly infected species are finches, African greys (15-20% of wild caught birds, Cockatoos 10-20% of wild caught birds and Eclectus parrots. . They absorb nutrients from host causing weight loss and diarrhea. A large number of worms can cause impaction. Some attribute it as a cause of feather plucking in African, Asian and Australian parrots (old word parrots).
Treatment - Praziquantel, Ivermectin.
Brand name : Wormout Gel(Aus), Ivpet plus.
Most common parasites found in birds housed in enclosures with access to ground or dirty cages and unhygienic food. Infections are very common in Budgerigars, Grass parakeets and Cockatiels. Clinical signs of severe infestation are distended abdomen, weight loss, diarrhea, impaction, Diagnosis is done through fecal examination/flotation. 
Treatment - Pyrantel pamoate, Fenbendazole.
Brand name : Wormout Gel(Aus), Ivpet plus.
They are tiny thread-like nematodes that affect the GI tract of most species of aviary birds, most commonly affecting Canaries, Budgerigars, and in Macaws. Symptoms may range from anorexia, vomiting and anemia. Diagnosis through fecal flotation or scraping of suspected lesions. 
Treatment - Mebendazole, Fenbendazole, Ivermectin.
Brand name : Wormout Gel(Aus), Ivpet plus.
Types of Lice and Mites
Biting Lice
These lice will cause itching and poor feather condition in birds. Parasites eggs can be seen attached to feathers. But most of this species are host specific and die quickly when they leave the host. I have not seen them on parrot species.
Treatment - Dusting with Pyrethrins will control infestation.
Treatment - Scatt, S76, Ivipet plus. Tix free.   
Scaly Face/Scaly feet Mite
One of the most common avian mite on pet birds. Causes dry scaly lesions on the bare skin of the face and feet. Very commonly found on Budgerigars and Canaries and in small sized parakeets.
Treatment – Scatt or Ivermection 0.01%
Brand Name Scatt, S76, Ivipet plus.
Air Sac Mites
These mites infect the trachea Gouldian finches and Canaries, Cockatiels and small parakeets.
The birds most affected are Canaries, finches (especially Lady Gouldians), parakeets and cockatiels. Air sac mite’s entire life cycle occurs in respiratory tract of infected host. Eggs spread by coughing or coughed, swallowed and passed in feces. Clinical signs include heavy open moth breathing, coughing, sneezing, nasal discharge. In severe form it can result in death due to asphyxiation. 
Treatment – Scatt, Ivermectin, clean environment to remove eggs that may be present and cause re-infection.
Treatment – Scatt or Ivermection 0.01% 
Brand Name Scatt, S76, Ivipet plus.
Red Mites
These mites are found to infect wild birds, birds housed in outdoor aviaries and pet stores. They feed on the blood leading to anemia, itchy skin and poor growth in young birds. These mites live in the cracks of the cages and nest boxes. They come out in the night and hide in the cracks during day. They are sometimes the cause of death of the nestlings in the nest. Diagnosis is by identification of mite, by through close inspection of cages, perches and nest boxes. One can check for red mites by placing a white towel or tissue paper in the corner of the cage or nest box during night. When check in the morning on can find the mites inside the folds of towel/tissue paper. 
Treatment – Dusting the cage, perches and nest boxes with Pyrethrins or commercially available anti-mite products . Scorching is also very effective and safe. 
Treatment - S7, Scatt ,Ivipet plus, Tix free.
Remember Parasites weaken the bird and its immune system making them susceptible to other infections as host they drain them of nutrition that is required for the wellbeing, this infections are usually over looked at the initial stage as they do not show any symptoms. Hence it is very important to quarantine an infected bird or a newly acquired bird of 30 days to reduce the risk the risk of transmission to healthy birds. 
Please note
 S76 is safe to use at any stage of their breeding cycle. It will not cause harm to the health and fertility of mature birds, fledglings or eggs.
Scatt is not recommended for use on birds younger that 6 months of age and during breeding season.
Referrance - Avian Medicine: Principles and Application by Ritchie, Harrison, Harrison).