Bond length is determined by the size of the bonded atoms and the multiplicity of the bond.

1. $\text{C-H}$: Hydrogen is the smallest atom, resulting in the shortest bond length ($107\text{ pm}$).
2. $\text{C=C}$: A double bond is shorter than a single bond due to greater orbital overlap and stronger attraction pulling the nuclei closer together ($133\text{ pm}$).
3. $\text{C-O}$: Oxygen has a smaller atomic radius than carbon, making the $\text{C-O}$ single bond ($143\text{ pm}$) shorter than a $\text{C-C}$ single bond.
4. $\text{C-C}$: A single bond between two carbon atoms has the longest bond length among these choices ($154\text{ pm}$). Therefore, the correct increasing order of bond lengths is $\text{C-H} < \text{C=C} < \text{C-O} < \text{C-C}$.