OmegaT is distributed under the GPL v3 license agreement.
Basically, that means that you have:
These 4 items are a good summary but you can also read the whole license.
OmegaT does not collect any user information and does not transmit any information without the explicit consent of the user.
The user or their project manager can set OmegaT to use online services. In that case, OmegaT shares information with online services:
OmegaT automatically checks the availability of newer versions on its development server without transmitting any user information, and the user can easily opt out in the Preferences settings.
If you find through your analysis that OmegaT communicates with an online service that you have not set, that would be a bug and we would ask you to report it.
The translatable data (ie. the files you are translating) are accessed to display the translatable contents to the user.
The translated data is stored in a file called project_save.tmx located in the omegat/ folder of any translation project. That file is compliant with the TMX specification, which is a standard used by most tools of the same category.
OmegaT does not store your information online (this is not a "cloud-based" product).