i have a player that likes to try creative ways to negate monsters that the party encounter. one tactic that he is starting to rely on is finding some way block a door that has a monster behind it. I am still a fairly new DM so i am still trying to find the line between creative approach to a situation and gaming the system. i am trying to see what other DMs would handle the situation.

one time he wanted to physically block a door with his body as he was fighting. in hind sight i figure i would give disadvantage on his attacks because he would have to keep his weight behind the door he is baring. i would have also let the goblin that the player had "locked" behind the door use a help action to help another attacking hobgoblin that was attacking the player.

in the most recent attempt, the player wanted to wedge an arrow into a trap door to block a tiger stuck on the other side. for that one i made him commit to the action and depending on how he rolled on a slight of hand check, it could have been a bonus action or action to make it work.

how would anyone else hand these or other similar scenarios, am i being too strict or too lax?

My personal take - I'd generally try to be supportive, because I'm always a fan of encouraging creative approaches to the game instead of having things be reduced to "I attack (roll attack + damage)." So if it makes sense, I'd allow the player to take that approach and adjudicate the results. I would generally look for a way to make this work and be plausible without being an easy win button.

one time he wanted to physically block a door with his body as he was fighting. in hind sight i figure i would give disadvantage on his attacks because he would have to keep his weight behind the door he is baring. i would have also let the goblin that the player had "locked" behind the door use a help action to help another attacking hobgoblin that was attacking the player.

So if I got this right, there was a door with a goblin behind it; the player wanted to shut the door and trap the goblin there. I would probably do one of the following two things:

Either 1) Have the player take an action to do it, describe it as them spending their action shoving the door closed with the goblin behind it. Then, each turn have the goblin use their action to try and escape - probably a contested strength/athletics check? - while the player gets to keep doing things on this side of a door, though they have to stay on the same space to keep holding the door shut.

Then, in the worst case, the player has spent an action to make the goblin waste an action, if the goblin makes their very first check. This is pretty decent already, not a great use of player's turn if the players are facing a bunch of goblins but not entirely a waste either. In the best case, if the goblin rolls poorly a few times,  the player has spent one action to make the goblin waste multiple actions - strong move.

Alternatively, 2) If you don't require them to use an action to do it, then it can't be as powerful. Making the player have disadvantage on attacks and dex and str saving throws while holding the door closed, and letting that goblin take the Help action against the player, seems like a reasonable penalty for taking one enemy partially out of the fight with no action cost. (I'd say as before, the goblin could instead use its action to try to force the door open by making a contested strength/athletics check.)

Basically, trying to figure out a way to make this work without breaking the action economy. Spending an action to deny the enemy one (or more) actions - seems fair. Doing something for free to impose a penalty on an enemy while also suffering some penalty - seems valid. Doing something for free that denies an enemy multiple actions.... ehhh... only if it clearly makes a lot of sense narratively, not if it's borderline.

in the most recent attempt, the player wanted to wedge an arrow into a trap door to block a tiger stuck on the other side. for that one i made him commit to the action and depending on how he rolled on a slight of hand check, it could have been a bonus action or action to make it work.

That makes sense - sleight of hand check to see how long it takes, valid. I'd also give the tiger a way to escape - probably using its action to make a strength check against some static DC (not a contested check in this case, since the player set a trap rather than actively holding it closed). DC set by how tough it is for the tiger to break through the door from the other side. Or you could have made it into effectively a contested check, with the sleight-of-hand check setting the DC for the tiger.

Again in this case, the worst case scenario would be to spend an action to make the monster waste an action (net benefit for the PCs if they outnumber the monsters, net cost if they don't) but the best case scenario is spend no actions to make the enemy waste multiple actions, which is pretty good for not using any limited resources like spell slots.

For comparison, take a 1st level spell like Tasha's Hideous Laughter. That spell lets you spend an action and a level 1 spell slot to make the enemy maybe waste its turn (if it fails a saving throw) or possibly multiple turns (if it fails multiple saves). But doesn't allow you to do much to the target without giving it more saving throws.

So IMO in all cases making the worst case scenario "spend an action to make the enemy waste an action" is already lower risk than many spells a wizard could spend slots casting. I'm ok with that, because I like encouraging my players to use the environment in clever ways. But it's just something to be wary of. If you're letting your martial characters use the environment in their favor to get bonuses, remember to also be generous if the spellcaster also wants to use a spell to interact with the environment and do something not exactly in the spell description.

If you want to be more strict, have one extra check happen at the beginning; either a contested check vs the goblin, or a straight check for the player or a saving throw for the goblin. If the "worst case scenario" is spend an action (for no benefit, if the goblin rolls well or you roll poorly) then that shifts the balance away from this and back towards more standard approaches. That's not necessarily a bad thing - "spend no resources besides an action, get no benefit if you roll poorly" is a pretty normal outcome for a turn, until players get high enough level to multiattack.

thanks for the advice, i will definitely be using the worst case scenario of action for action as a guideline in adjudications.

Also keep in mind what material the door is made of. The DMG has a list of HP/AC pertaining to specific materials. Goblin can use 2 turns doing contested checks to try and push the door open vs the PC trying to push the door closed. After that the other side of the door goes quiet. PC doesn't know what is happening, but the goblins can use methods to break down doors with force and/or fire. Or have a goblin keep pushing as a distraction while others use escape/secret tunnels to get around the door to the PC's. The PC is still buying time for some preparations as a reward for creativity. And they better make use of that borrowed time. Goblins are cannibalistic, tribal, fierce and cowardly so they're not the best example to be used here. Other enemies wouldn't be stopped by a mere door blockade. They'd just throw alchemist fire and destroy that wooden door. Or hack it to pieces and peek through like The Shining or use other means.

Action: Hold the Door. Make a strength check of a DC appropriate for the situation. If successful, the character may continue to use their action each turn to hold the door, keeping out creatures on the other side until the strength check fails or until the door is destroyed.

In addition to the other suggestions with the door scenario, you could alternatively calculate their AC without their Dex bonus (doesn't work on Heavy Armor) or give them disadvantage on or automatically fail dex saves. The reasoning for this would be their inability to effectively move without allowing the door to open. Between this and what you had suggested, the character is restrained.

If they choose to move, the door flies open. It catches then as they are leaving the space and deals 1d4 (or some appropriate amount) bludgeoning damage. This is in addition to the effects of the attack made on them. 

Easiest way to resolve requests is to ask "how?"

"How are you going to barricade that door?"

Let them tell you what they want to do and how they're going to try and do it. Then, work out what actions and skill rolls they need to take to achieve that. Then, get the mobs to challenge those rolls (e.g beating down the barricaded door).

For situation 1, I think that is a good assessment (assuming he is trying to hold the door by leaning back on it while fighting).

For situation 2, I would just make it an action (not bonus) and use an Athletics or Slight of Hand roll to set how hard it is to dislodge.

Seems like you are doing a good job of adjudicating on the fly.

This could be an Athletics check to hold the door close vs. the bad guy's check.

It could also be an Intelligence check to successfully bar the door with an object or item. Or a Sleight of Hand check to jam the lock...