This question was phrased such that it asks for opinions.
Opinion #1 Animals deserve to be protected from those who would neglect them or deliberately mistreat them. These are not "rights", but a legal requirement for their owners to provide them with proper protection and care.
They should have rights.
Opinion #2While animals deserve reasonable protection against abuse, they do not have legal "rights" in the same way humans do. The US courts have upheld the concept that with the granting of rights also comes the responsibility of duties. Since animals cannot reasonably be expected to carry out any duties, they are also accordingly denied rights.
This does not give humans any legal standing in cases of abuse. In the same way animals cannot have rights, humans DO have duties and responsibilities. Most US communities do not allow a person to have a poorly kept, extremely unkempt or dangerous residence; similarly, humans are not allowed to abuse animals to the point of starvation, thirst, disease, and/or death.
Cases of alleged abuse are normally handled by local law enforcement with the possible assistance of animal welfare agencies.
Opinion #3Animals should not have Human Rights BEFORE or IF we ever invent a device that can help us communicate with them.
That depends on what you mean, are there any rights that are recognize and made into law? Not really, there are laws protecting very select animals, and they aren't very good ones, but sentient beings all have rights whether it is reflected in law or not.