What I'm going to say is going to draw a LOT of flak, but this tactic worked well for me in my early days, when I struggled with keeping up.
If you're massively behind, as in the scenarios you described, sometimes catching up is not a viable option. In this case, the best strategy is to try and use your character's worthlessness to your team's advantage.
Having been killed a lot, your deaths will give your opponents less gold. Since you're presumably at a lower level, you'll grant less experience and you'll respawn slightly faster. This means you can perform kamikaze strategies with less risk and loss.
If your teammates are losing a fight, use as much CC as you can to let them get away, dying in their place.
If your team is unsure about an area, scout ahead. Attempt Baron/Dragon steals whenever possible.
If a tower is low on health and undefended, you can volunteer to backdoor it. You'll at worst inflict a bit of damage on the tower, and at best either destroy it or force some members of the enemy team to deal with you. This allows for the rest of your team to push separately.
An important consideration to keep in mind when using a strategy such as this is that you must never get a kill, as this will reset your gold bounty, dramatically increasing the potential enemy gains from killing you.