変てこ is a shortened form of 変てこりん, which seems to have underwent phonological change from 変ちくりん. Not sure about the motivation of the sound change, but does not look unreasonable. The vowels in ちく changed:
[iu] → [eo], which is:
[+high, -back][+high, +back] → [-high, -back][-high, +back]
The origin of ちくりん is unknown, but is used with a few na-adjectives such as
変ちくりん
珍ちくりん
妙ちくりん
But be careful because some of them are politically incorrect.
ちくりん can be considered as a diminutive, adding cuteness. 変な does not have that cuteness nuance. 変てこ, 変てこりん, and 変ちくりん imply funny thing that is human made and cannot be used in a serious situation, whereas 変な simply means strange or unusual.
Scene: A doctor is doing a surgery, and finds an unusual thing in the patients body.
In this case, the doctor can say 変なものがある, but definetely not 変てこなものがある.
Scene: There is a painting on the wall, which is commical and fun but nothing wrong.
In this case, although 変な絵がある is not impossible, 変てこな絵がある will be a better fit.
As Tsuyoshi Ito mentions in the comment, へなちょこ means poor in quality. It does not mean strange.
