TL;DR: Your creature is a 0/0 Elemental creature with X +1/+1 counters and Haste. No Land type, no tapping for mana-ability, no original creature type.
In the answer below, I've tried to look at the state of the creature through-out the whole process of Imprisonment, Awakening and breaking out of Imprisonment, to keep track of all the things happening to it, and all the rules applied. Not all of this information is relevant to the answer per sé, but in my opinion this does cover all bases - it makes clear why the effects happen as described.
So, we have a creature - let's call it Charlie - that becomes a land, then becomes a creature again with an effect stating "it's still a land".
Imprisoned in the Moon is a continuous type-changing effect, lasting for as long as the creature is enchanted. When looking at the card, the game considers it a land after layer 4 (613.1d) is processed:
613.1d Layer 4: Type-changing effects are applied. These include effects that change an object’s card type, subtype, and/or supertype.
Imprisoned in the Moon also grants Charlie the ability to tap for mana:
Enchanted permanent is a colorless land with "{T}: Add Colorless to your mana pool" and loses all other card types and abilities.
Then we play the Awaken spell. Charlie is a land that can tap for colorless mana, and after receiving the +1/+1 counters, also a 0/0 creature with X +1/+1 counters on it, and haste. Imprisoned in the Moon tries to strip all other abilities off of it, but since both Imprison and Awaken generate ability-altering effects they collide on layer 6 (613.1f)). The Awaken takes precedence because it has a later timestamp:
613.6. Within a layer or sublayer, determining which order effects are applied in is usually done using a timestamp system. An effect with an earlier timestamp is applied before an effect with a later timestamp.
So, Charlie is a creature again! Note that it can still tap for mana; Imprison is still on Charlie and the Awaken doesn't strip the mana-tap ability (in fact, it even confers this implicit ability from a regular forest onto an Elemental X/X, if we'd targeted a Forest with Awaken instead of dear Charles). Note that at this point, Charlie is equally vulnerable to Terror as to Rancid Earth.
Now the interesting bit: Imprisoned in the Moon is removed. Will it remove the Land type? Yes. Charlie doesn't have another effect granting him the Land type. Imprison made Charlie into a Land, but since Imprison is removed, its continuous type-changing effect stops as well:
611.3. A continuous effect may be generated by the static ability of an object.
[...]
611.3b The effect applies at all times that the permanent generating it is on the battlefield[...]
Since Imprison is no longer on the battlefield, the type-changing effect stops. Awaken states Charlie 'is still a land', but that is not a source, merely a conduit:
205.1. The type line is printed directly below the illustration. It contains the card’s card type(s). It also contains the card’s subtype(s) and supertype(s), if applicable.
205.1a Some effects set an object’s card type. In such cases, the new card type(s) replaces any existing card types. Counters, effects, and damage marked on the object remain with it[...]
205.1b Some effects change an object’s card type, supertype, or subtype but specify that the object retains a prior card type, supertype, or subtype. In such cases, all the object’s prior card types, supertypes, and subtypes are retained. This rule applies to effects that use the phrase “in addition to its types” or that state that something is “still a [type, supertype, or subtype].”[...]
The other effects from Awaken still apply: Charlie is an Elemental and he retains his +1/+1 counters as shown by the emphasised bit of rule 205.1a above; his base P/T is 0/0 and Awaken still grants him Haste.
Sidenote: if by some other effect, Charlie would retain the Land type, he could no longer tap for (colorless) mana, because that ability too is only sourced by the Imprison.