Eternal Life

I'm listening to Chuck Swindoll today. Good message on Death. (It has an English accent when spoken aloud.)
Always excellent teaching but today I couldn't get past this one thing. In his message he repeated this oft-repeated Evangelicalism:

There is a sense in which everybody has eternal life because everybody is going to spend eternity somewhere. Those who have accepted Jesus Christ will spend eternity in Heaven and those who have not accepted Him are going to spend eternity in Hell.

But John 3:16 (also an oft-repeated Evangelicalism) indicates that eternal life, zoe aionios, is something in God through the Son that we have. We don't have eternal life and then we gain eternal life through believing in the Son. In fact John goes on to day that those who don't believe live in death.

I tell you the truth, whoever hears my word and believes him who sent me has eternal life and will not be condemned; he has crossed over from death to life. I tell you the truth, a time is coming and has now come when the dead will hear the voice of the Son of God and those who hear will live. For as the Father has life in himself, so he has granted the Son to have life in himself. -Jesus the Christ, John 5:24-26

Where do we go with this?

• In what sense is it "eternal life" for those in Hell?
• Is it the fact that it is LIFE or that it is ETERNAL matter more?
• Does the "crossing over from death to life" have a present sense? How?

Maybe we should stop quickly repeating things we hear on the radio.