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
[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
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
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.