Woody is scared of everything, and is not very good at doing contests. Because of his panphobic personality and inability to do a lot of contests, he is hated by a lot of contestants. He was dead in BFDIA, so his interactions with everyone ended at that time, until he was recovered in IDFB.
TB told Teardrop to calm down when she kicked Woody because Woody is made of balsa wood, a kick could severely injured him.
TB kicked Rocky out of the way in Episode 2 in order to not cause a collision between the two.
Though it may just be a coincidence, both Woody and TB were abducted by the spaceship in Return of the Hang Glider. Later in that episode, Tennis Ball said Woody had "a heart attack" and died.
Eraser talked about how he can't stand Woody and how Woody is a scaredy-cat in Take the Plunge: Part 1 and he is "so uncool". Eraser, along with everyone else, wasn't too happy when Woody got on their team. Eraser got angry at Leafy/Woody when Leafy said Woody could have some of her cake for free in Episode 4.
Status: Minor Enemies
Blocky kicked Woody in Episode 1 because he wanted to hurt somebody.
Blocky also kicked Woody again in The Glistening when he found out Woody got more votes than him to rejoin (5 votes).
Woody had a crush on TD in Episode 1, but was kicked away when Teardrop got angry. Since then, the two have not gotten any interaction. However, you can see them staring at each other when they're in the TLC (this might be only because of their idling pose, however).
Status: Minor Enemies/Love interest (Woody's side)
Match and Woody ended up on the same team in Episode 1. The two of them were seen standing on Spongy during the last few seconds of Take the Plunge: Part 2, along with Firey and a lot of the Squashy Grapes members. Match paid for Woody to get cakes in Sweet Tooth.
Status: Minor Friends
In Take the Plunge: Part 1, when Woody landed from Blocky's kick, Leafy helps him up and told Woody to enjoy life in.
In Take the Plunge: Part 2, When it was time to choose teams, Leafy said sorry to Woody and chose Rocky instead.
In Sweet Tooth, Leafy told Woody he could have cake for free, angering Pen and Eraser.
Woody voted for Leafy in Return of the Hang Glider to win, and slapped Needle and Match for not voting for Leafy.
Pin was very upset when she had to choose Woody to be on her team, and barfed on him.
In Barriers and Pitfalls, she kicked him away when Woody tried to climb over her.
In Are You Smarter Than a Snowball?, she kicked Woody for having testophobia, while no one else have it.
However, in Welcome Back, Pin didn't mind when Woody stumbled into the group, despite hating him so much. She also showed concern for Woody when he was on fire.
Status: Major Enemies
Woody bumped into Rocky in Episode 1. Woody had a piece chipped off of him and then Woody screamed at a rate of 120-150 decibels. A "Woody and Rocky collision" is when Woody and Rocky collide with each other. Either of them could break, but the one who has faster reactions and lower damage is Woody, surprisingly. Rocky will break after 15 minutes from the collision. (Part of this is just a theory made by Golf Ball and Tennis Ball to explain why Woody and Rocky are just the weirdest couple.)
Status: Major Enemies
In Half a Loaf is Better Than None, when Woody drowns in the loaf, the Announcer laughs.
In The Glistening, Woody voted for Ice Cube to be eliminated, along with most of the contestants.
In Welcome Back, Ice Cube saved Woody when he was on fire by jumping in, causing her to melt.