How long would it take for them to join me?

The oldest 1 will age out but will go into a different family-based preference category that just takes longer to qualify for a visa under the current immigration laws. The other two should be fine. For them the process will take about 2-3 years before they will qualify for immigrant visas.

As of right now, the process takes 2 years, from filing of the petition to a visa number becoming available (consular processing takes from weeks to several months, depending on the country). It is likely that your younger children will get their immigrant visas before they turn 21; but the 20 year old might not make it through the process in time. The law "stops the clock" on a child's age from the date of the petition's filing through the date of its approval. It means that, if your child is, let's say 20 years and 3 months today, and you file the petition tomorrow, and USCIS takes, say, 20 months to approve the petition, and an immigrant visa becomes available to your child in exactly 2 years from now, on May 23, 2015, your child will be considered to be 20 years and 7 months on that date - the 20 months that passed while USCIS was working on your petition will be deducted out of your child's actual age. Since 20 months is the real time that USCIS takes today to work on an I-130 petition, your older child might have a chance.

Your oldest child might age out as the current wait time is roughly two years. Thus, you should file right away for all three children. If the oldest one does age out, at least the clock will still be running in that child's favor. The adult children of U.S. residents (21 and older) must wait a long time; the current priority date for most countries is July 2005, which means that the USCIS now is processing those petitions that were filed back in 2005. That tells you how long the wait is for the adult children.

Since your children are all below 21, if you file their petition now, the petition will classified under F2A category. The estimated waiting time for F2A category is approximately 2 years, so the oldest is likely to age out. The only way the oldest can retain his/her child category is if he/she will benefit under the Child Status Protection Act (CSPA). Otherwise, the age out child will rollover to F2B category (assuming you are still a green card holder and your child is not married) in which case the waiting time is longer. See below.

You must file an I-130 petition for each child and I suggest you do so right away. In that category F2 [child of a green card holder], the average processing time is about 2 years. For instance, visas filed by green card holders for their children that are now being processed were filed Jun 2011. Your fear about the children aging out is unwarranted. Rest assured as long as the petitions are filed before each child's 21st birthday, they will be fine. In the interim, you may also wish to consider other options under which your children can come to the US in a shorter period of time. For this, you will need to consult with an experienced immigration lawyer