Use 'invite along' for casual events or outings, not formal or official events. I'm hanging out at the park later, do you want me to invite you along?
Pro Tip 2/3
Personal Choice
It implies that attending the event is optional and based on the person's preference. They're going bowling this Saturday; feel free to invite them along if they're interested.
Pro Tip 3/3
Group Activities
Often used when the event involves a group, thus making it more social. We're all meeting up for lunch; do you want to invite Alex along?