Take a breather, I know, it's frustrating. Most 1 yr olds are VERY Active and don't like being con/restrained, especially those who've mastered crawling or walking. Offer a reward (small, quiet toy or a game of peek-a-boo, healthy foods he likes during meals or something sweet after the meal, short trip, etc.) for sitting still (or not trying to get out) even shortly, or a distraction, a toy or cherished item he likes while sitting. Make him feel calm relaxed w/no TV, radio, or other noises that he may find interesting while eating, strolling around. If he likes you to rub his head/hair or play 'this little piggy,' do so occasionally during the meal or short trip. Find ways to make the space (high chair, stroller, etc.) attractive with something he likes. Most of all, relax, be patient. The more uptight you are, the baby will match your frustration (and vice versa). Talk to him calmly while putting him in, make up a song to make it fun. Make a game of it! Take breaks (2min in, 2min out, etc. if at all possible). Do what he can stand and gradually increase it. If this is your first child, you may not realize that the 30 or so minutes you and hubby are used to at the dinner table or casual stroll is not the same for a 0ne-year old, yet. The rewards will keep him interested. Don't make the restraints too tight as these could hurt him. If you feel he's way too active than what's expected, check w/your doctor. Maybe he's not getting enough sleep, is too stimulated, or has other developmental concerns although I HIGHLY DOUBT IT if all else is OK. Best of luck. I hope it works out!
This is normal! Most kids go thru phases! One minute they can't stand something and before you know it, they're doing or eating the very thing they couldn't tolerate (and vice versa)! I bet he'll grow into tolerating the high chair, stroller to SOME degree over a short time.