I don't think you'll have much to worry about regarding whether the two ostriches running loose on the ranch will eat quail or turkey eggs. Those nest are generally so well hidden that an ostrich would only stumble upon one by sheer luck. If one of the ostriches did stumble upon such a nest, it might peck at the eggs more out of curiosity than to eat them. I have seen ostriches eat pecans and acorns, so a small quail egg might cause them to pick up one or two, again out of curiosity. But to answer your question, ostriches are grazers that mostly eat plants and seeds. They are classified as omnivores because they have been seen to eat small lizards, bugs, etc. I really doubt they will bother the quail or turkeys because ostriches don't naturally seek out such things to eat or chase them down to catch them. In fact, your ranch may produce more wild turkey and quail offspring due to the ostriches' deterrent effect upon predators. However, if you continue to have concerns, please contact the AOA or a member and hopefully a new home can be found for the two ostriches if you wish to have them removed from the ranch.
We found 2 feral ostriches on our ranch in central Texas. My only concern with them being there is if they will eat turkey eggs, turkey nestling or quail or quail babies. Does anyone know if this is likely?