What are the type advantages and disadvantages in Digimon World: Dawn/Dusk?

Before getting to the answer, there is a bit of relevant background information - namely, there is a difference between Digimon families/species and Digimon elements.

Families: Every Digimon in the game is part of a family. The 8 family types are as follows:

• Holy
• Demon
• Plant/Insect
• Machine
• Beast
• Dragon
• Water/Aquatic
• Bird

This is a trait that you as a player can know upon encountering different Digimon. This will not differ between the same species of Digimon (for example, all Chicchimon will be part of the holy family)

Elements:

Every attack has an element type. There are also 8 of these:

• Holy
• Dark
• Electric
• Steel
• Earth
• Air
• Water
• Fire

Digimon of the same family will usually use that type of element to attack:

• Holy family typically uses holy element attacks
• Demon family typically uses dark element attacks
• Plant/Insect will typically use electric element attacks
• Machine family will typically use steel element attacks
• Beast family will typically use earth element attacks
• Dragon family will typically use fire element attacks
• Water family will typically use water element attacks
• Bird family will typically use air type attacks

Every Digimon has an elemental weakness, though it varies by individual Digimon. A total list for all Digimon, including species/family, strengths, and weaknesses can be found here

However, regarding specific elemental attack type weaknesses, according to this thread, every Digimon:

has a hidden Resistance status for each element, the lowest value is their "weakness" and the highest one their "resistant" one. Obviously hitting something with something it's weak against deals more damage.

So, although you can know a specific Digimon's type weakness (from the total list of all Digimon above), the remainder type weaknesses are hidden. Nevertheless, all of these hidden values can be buffed using farm items, though I believe that they still remain hidden.

The only way that comes to mind to test a specific Digimon's other weaknesses would be trial and error. I would suggest keeping an eye out for attack types that are very effective against your specific Digimon, and then buffing that resistance with a farm item.