Orthodoxy in Christianity is the holding to the oldest beliefs. It is of course impossible for the religion not to evolve at all as new questions and there answer have to addressed. The "Orthodox" version is often considered to be the least evolved sect of a religion. Does the concept of Orthodox apply in Hinduism?
Today all most all of Hinduism is Orthodox. Due to the classification of Buddhism and Jainism as separate religion they are no longer treated as part of Hinduism. Hence, as what is left in Hinduism is being primarily based on the Vedas (the revealed scriptures) all of Hinduism is orthodox.
The definition of unorthodox in Hinduism is Veda neendako nâstikaha. That is, the school of thought that doesn't accept authority of the Vedas is unorthodox. Previously Buddhism, Jainism and Ajivika school of thought came into formation in India by rejecting the Vedas, hence they were considered unorthodox. But after their classification as separate religion, most of Hinduism is Orthodox except certain sects that follow scriptures that are not based on the Vedas.
It is hard to classify Hinduism as Orthodox & Heterodox. Hinduism has always been fluid with many Sampradayas(traditions/philosophical views) existing at the same time and evolving together.
With respect to Christianity, the religion was centrally controlled and codified and what prevailed became Orthodoxy(all sects which subscribe to Nicene Creed are actually orthodox) and other views became Heratical and was sidelined. This was not the case with Hinduism as Hinduism was a highly de-centralized tradition and every view was allowed to grow and flourish.
There are historians who incorrectly classify the Āstika darshanas(Nyāyá,Vaiśeṣika, Sāṃkhya, Yoga, Mimāṃsā, Vedanta) as orthodox & Nāstika darshanas(Jain, Buddhist, Cārvāka) as Hetrodox. But this labeling is incorrect since each darshana had a different notion of who was an Āstika and who was a Nāstika.
While there is no single school of thought that is called "Orthodox Hinduism", there are six schools of thought that are lowercase-o "orthodox Hinduism". These are called the āstika schools (the conventional translation is indeed "orthodox"), and they are contrasted with the "unorthodox" nāstika schools. The āstika schools are those that accept the Vedas as authoritative; the nāstika schools are those that do not.
Some of the nāstika schools are well-known to the wider world - the term nāstika is primarily applied to traditions that originated in Hinduism, but that we would not today view as Hindu, e.g. the Buddhists and the Jains. The extinct Charvaka school is also considered nāstika. The āstika schools are not so well-known among non-Hindus: they are Samkhya, Yoga, Nyaya, Vaiseshika, Mimamsa, and Vedanta.
Note that this classification is an external classification - it reflects an outside observer's position on what constitutes orthodoxy and heterodoxy in the context of Hinduism. It does not reflect the internal view of Hindu groups on one another - some of the āstika groups will consider other āstika groups to be nāstika, and so forth.
So in sum, yes - the concept of orthodoxy exists in Hinduism, though it isn't really all that similar to the idea of Orthodox Christianity.