Just talk to your financial planner they should be able to explain what you need to do. Usually there are no time constraint if so the company is why as in your situation. The 401 K rollover is ideal because it will allow you to transfer all 3 of your existing retirement account into a new retirement account without being subject to unnecessary taxes or withdrawal penalties, this is the ideal plan for you it would seem like.

Find out from the new agency what the permissible actions are with the new 401(k) Plan. Do they accept Rollovers from other 401(k) accounts? If so, get cracking on setting those "Trustee-to-Trustee" Transfers from the old to the new.

Otherwise, in general, there are no set-in-stone time constraints for combining multiple 401(k) accounts. Theoretically you can have several 401(k) accounts from numerous agencies/past employers well into your Retirement. Granted, it is considered easier to watch over your accounts if they are all in 1 account.

Check each of your Plans' SPD (Summary Plan Description) documents to get a better idea of what is and is not allowed with each Plan. And, yes, each 401(k) can be quite a bit different in some of the finer areas (like taking money out in special situations, for example).
If you need help, search for a Financial Planner with special emphasis in Retirement Plans.