Elude means "evade or escape," like the way you might elude the other kids during a game of hide-and-seek. This word can also mean "to be hard to understand." No matter how hard you try, the finer points of quantum physics might elude you.
Elude has a slippery feeling to it. You elude the police, math can elude you — and that yak you went to see on safari but never got a glimpse of, you might say that he has eluded you as well. Delude means "to deceive," and there are times when someone can both delude and elude you — like when the conman took your money and then escaped out the back door.